Papers
Topics
Authors
Recent
Search
2000 character limit reached

Multidepot Capacitated Vehicle Routing with Improved Approximation Guarantees

Published 27 Aug 2023 in cs.DS | (2308.14131v3)

Abstract: The Multidepot Capacitated Vehicle Routing Problem (MCVRP) is a well-known variant of the classic Capacitated Vehicle Routing Problem (CVRP), where we need to route capacitated vehicles located in multiple depots to serve customers' demand such that each vehicle must return to the depot it starts, and the total traveling distance is minimized. There are three variants of MCVRP according to the property of the demand: unit-demand, splittable and unsplittable. We study approximation algorithms for $k$-MCVRP in metric graphs, where $k$ is the capacity of each vehicle. The best-known approximation ratios for the three versions are $4-\Theta(1/k)$, $4-\Theta(1/k)$, and $4$, respectively. We give a $(4-1/1500)$-approximation algorithm for unit-demand and splittable $k$-MCVRP, and a $(4-1/50000)$-approximation algorithm for unsplittable $k$-MCVRP. When $k$ is a fixed integer, we give a $(3+\ln2-\max{\Theta(1/\sqrt{k}),1/9000})$-approximation algorithm for the splittable and unit-demand cases, and a $(3+\ln2-\Theta(1/\sqrt{k}))$-approximation algorithm for the unsplittable case.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (28)
  1. Asano, T., Katoh, N., Tamaki, H., Tokuyama, T.: Covering points in the plane by k-tours: Towards a polynomial time approximation scheme for general k. In: STOC 1997, pp. 275–283 (1997) Haimovich and Kan [1985] Haimovich, M., Kan, A.H.G.R.: Bounds and heuristics for capacitated routing problems. Mathematics of Operations Research 10(4), 527–542 (1985) Altinkemer and Gavish [1987] Altinkemer, K., Gavish, B.: Heuristics for unequal weight delivery problems with a fixed error guarantee. Operations Research Letters 6(4), 149–158 (1987) Christofides [1976] Christofides, N.: Worst-case analysis of a new heuristic for the travelling salesman problem. Technical report, Carnegie-Mellon University (1976) Serdyukov [1978] Serdyukov, A.I.: Some extremal bypasses in graphs. Upravlyaemye Sistemy 17, 76–79 (1978) Karlin et al. [2021] Karlin, A.R., Klein, N., Gharan, S.O.: A (slightly) improved approximation algorithm for metric TSP. In: STOC 2021, pp. 32–45 (2021) Karlin et al. [2023] Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Haimovich, M., Kan, A.H.G.R.: Bounds and heuristics for capacitated routing problems. Mathematics of Operations Research 10(4), 527–542 (1985) Altinkemer and Gavish [1987] Altinkemer, K., Gavish, B.: Heuristics for unequal weight delivery problems with a fixed error guarantee. Operations Research Letters 6(4), 149–158 (1987) Christofides [1976] Christofides, N.: Worst-case analysis of a new heuristic for the travelling salesman problem. Technical report, Carnegie-Mellon University (1976) Serdyukov [1978] Serdyukov, A.I.: Some extremal bypasses in graphs. Upravlyaemye Sistemy 17, 76–79 (1978) Karlin et al. [2021] Karlin, A.R., Klein, N., Gharan, S.O.: A (slightly) improved approximation algorithm for metric TSP. In: STOC 2021, pp. 32–45 (2021) Karlin et al. [2023] Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for unequal weight delivery problems with a fixed error guarantee. Operations Research Letters 6(4), 149–158 (1987) Christofides [1976] Christofides, N.: Worst-case analysis of a new heuristic for the travelling salesman problem. Technical report, Carnegie-Mellon University (1976) Serdyukov [1978] Serdyukov, A.I.: Some extremal bypasses in graphs. Upravlyaemye Sistemy 17, 76–79 (1978) Karlin et al. [2021] Karlin, A.R., Klein, N., Gharan, S.O.: A (slightly) improved approximation algorithm for metric TSP. In: STOC 2021, pp. 32–45 (2021) Karlin et al. [2023] Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Christofides, N.: Worst-case analysis of a new heuristic for the travelling salesman problem. Technical report, Carnegie-Mellon University (1976) Serdyukov [1978] Serdyukov, A.I.: Some extremal bypasses in graphs. Upravlyaemye Sistemy 17, 76–79 (1978) Karlin et al. [2021] Karlin, A.R., Klein, N., Gharan, S.O.: A (slightly) improved approximation algorithm for metric TSP. In: STOC 2021, pp. 32–45 (2021) Karlin et al. [2023] Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Serdyukov, A.I.: Some extremal bypasses in graphs. Upravlyaemye Sistemy 17, 76–79 (1978) Karlin et al. [2021] Karlin, A.R., Klein, N., Gharan, S.O.: A (slightly) improved approximation algorithm for metric TSP. In: STOC 2021, pp. 32–45 (2021) Karlin et al. [2023] Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Karlin, A.R., Klein, N., Gharan, S.O.: A (slightly) improved approximation algorithm for metric TSP. In: STOC 2021, pp. 32–45 (2021) Karlin et al. [2023] Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  2. Haimovich, M., Kan, A.H.G.R.: Bounds and heuristics for capacitated routing problems. Mathematics of Operations Research 10(4), 527–542 (1985) Altinkemer and Gavish [1987] Altinkemer, K., Gavish, B.: Heuristics for unequal weight delivery problems with a fixed error guarantee. Operations Research Letters 6(4), 149–158 (1987) Christofides [1976] Christofides, N.: Worst-case analysis of a new heuristic for the travelling salesman problem. Technical report, Carnegie-Mellon University (1976) Serdyukov [1978] Serdyukov, A.I.: Some extremal bypasses in graphs. Upravlyaemye Sistemy 17, 76–79 (1978) Karlin et al. [2021] Karlin, A.R., Klein, N., Gharan, S.O.: A (slightly) improved approximation algorithm for metric TSP. In: STOC 2021, pp. 32–45 (2021) Karlin et al. [2023] Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for unequal weight delivery problems with a fixed error guarantee. Operations Research Letters 6(4), 149–158 (1987) Christofides [1976] Christofides, N.: Worst-case analysis of a new heuristic for the travelling salesman problem. Technical report, Carnegie-Mellon University (1976) Serdyukov [1978] Serdyukov, A.I.: Some extremal bypasses in graphs. Upravlyaemye Sistemy 17, 76–79 (1978) Karlin et al. [2021] Karlin, A.R., Klein, N., Gharan, S.O.: A (slightly) improved approximation algorithm for metric TSP. In: STOC 2021, pp. 32–45 (2021) Karlin et al. [2023] Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Christofides, N.: Worst-case analysis of a new heuristic for the travelling salesman problem. Technical report, Carnegie-Mellon University (1976) Serdyukov [1978] Serdyukov, A.I.: Some extremal bypasses in graphs. Upravlyaemye Sistemy 17, 76–79 (1978) Karlin et al. [2021] Karlin, A.R., Klein, N., Gharan, S.O.: A (slightly) improved approximation algorithm for metric TSP. In: STOC 2021, pp. 32–45 (2021) Karlin et al. [2023] Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Serdyukov, A.I.: Some extremal bypasses in graphs. Upravlyaemye Sistemy 17, 76–79 (1978) Karlin et al. [2021] Karlin, A.R., Klein, N., Gharan, S.O.: A (slightly) improved approximation algorithm for metric TSP. In: STOC 2021, pp. 32–45 (2021) Karlin et al. [2023] Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Karlin, A.R., Klein, N., Gharan, S.O.: A (slightly) improved approximation algorithm for metric TSP. In: STOC 2021, pp. 32–45 (2021) Karlin et al. [2023] Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  3. Altinkemer, K., Gavish, B.: Heuristics for unequal weight delivery problems with a fixed error guarantee. Operations Research Letters 6(4), 149–158 (1987) Christofides [1976] Christofides, N.: Worst-case analysis of a new heuristic for the travelling salesman problem. Technical report, Carnegie-Mellon University (1976) Serdyukov [1978] Serdyukov, A.I.: Some extremal bypasses in graphs. Upravlyaemye Sistemy 17, 76–79 (1978) Karlin et al. [2021] Karlin, A.R., Klein, N., Gharan, S.O.: A (slightly) improved approximation algorithm for metric TSP. In: STOC 2021, pp. 32–45 (2021) Karlin et al. [2023] Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Christofides, N.: Worst-case analysis of a new heuristic for the travelling salesman problem. Technical report, Carnegie-Mellon University (1976) Serdyukov [1978] Serdyukov, A.I.: Some extremal bypasses in graphs. Upravlyaemye Sistemy 17, 76–79 (1978) Karlin et al. [2021] Karlin, A.R., Klein, N., Gharan, S.O.: A (slightly) improved approximation algorithm for metric TSP. In: STOC 2021, pp. 32–45 (2021) Karlin et al. [2023] Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Serdyukov, A.I.: Some extremal bypasses in graphs. Upravlyaemye Sistemy 17, 76–79 (1978) Karlin et al. [2021] Karlin, A.R., Klein, N., Gharan, S.O.: A (slightly) improved approximation algorithm for metric TSP. In: STOC 2021, pp. 32–45 (2021) Karlin et al. [2023] Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Karlin, A.R., Klein, N., Gharan, S.O.: A (slightly) improved approximation algorithm for metric TSP. In: STOC 2021, pp. 32–45 (2021) Karlin et al. [2023] Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  4. Christofides, N.: Worst-case analysis of a new heuristic for the travelling salesman problem. Technical report, Carnegie-Mellon University (1976) Serdyukov [1978] Serdyukov, A.I.: Some extremal bypasses in graphs. Upravlyaemye Sistemy 17, 76–79 (1978) Karlin et al. [2021] Karlin, A.R., Klein, N., Gharan, S.O.: A (slightly) improved approximation algorithm for metric TSP. In: STOC 2021, pp. 32–45 (2021) Karlin et al. [2023] Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Serdyukov, A.I.: Some extremal bypasses in graphs. Upravlyaemye Sistemy 17, 76–79 (1978) Karlin et al. [2021] Karlin, A.R., Klein, N., Gharan, S.O.: A (slightly) improved approximation algorithm for metric TSP. In: STOC 2021, pp. 32–45 (2021) Karlin et al. [2023] Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Karlin, A.R., Klein, N., Gharan, S.O.: A (slightly) improved approximation algorithm for metric TSP. In: STOC 2021, pp. 32–45 (2021) Karlin et al. [2023] Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  5. Serdyukov, A.I.: Some extremal bypasses in graphs. Upravlyaemye Sistemy 17, 76–79 (1978) Karlin et al. [2021] Karlin, A.R., Klein, N., Gharan, S.O.: A (slightly) improved approximation algorithm for metric TSP. In: STOC 2021, pp. 32–45 (2021) Karlin et al. [2023] Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Karlin, A.R., Klein, N., Gharan, S.O.: A (slightly) improved approximation algorithm for metric TSP. In: STOC 2021, pp. 32–45 (2021) Karlin et al. [2023] Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  6. Karlin, A.R., Klein, N., Gharan, S.O.: A (slightly) improved approximation algorithm for metric TSP. In: STOC 2021, pp. 32–45 (2021) Karlin et al. [2023] Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  7. Karlin, A.R., Klein, N., Gharan, S.O.: A deterministic better-than-3/2 approximation algorithm for metric TSP. In: IPCO 2023. Lecture Notes in Computer Science, vol. 13904, pp. 261–274 (2023) Blauth et al. [2022] Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  8. Blauth, J., Traub, V., Vygen, J.: Improving the approximation ratio for capacitated vehicle routing. Mathematical Programming, 1–47 (2022) Friggstad et al. [2022] Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  9. Friggstad, Z., Mousavi, R., Rahgoshay, M., Salavatipour, M.R.: Improved approximations for capacitated vehicle routing with unsplittable client demands. In: IPCO 2022. Lecture Notes in Computer Science, vol. 13265, pp. 251–261 (2022) Bompadre et al. [2006] Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  10. Bompadre, A., Dror, M., Orlin, J.B.: Improved bounds for vehicle routing solutions. Discrete Optimization 3(4), 299–316 (2006) Zhao and Xiao [2022] Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  11. Zhao, J., Xiao, M.: Improved approximation algorithms for capacitated vehicle routing with fixed capacity. CoRR abs/2210.16534 (2022) Li and Simchi-Levi [1990] Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  12. Li, C., Simchi-Levi, D.: Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2(1), 64–73 (1990) Harks et al. [2013] Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  13. Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013) Rathinam et al. [2007] Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  14. Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Transactions on Automation Science and Engineering 4(1), 98–104 (2007) Xu et al. [2011] Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  15. Xu, Z., Xu, L., Rodrigues, B.: An analysis of the extended christofides heuristic for the k-depot tsp. Operations Research Letters 39(3), 218–223 (2011) Xu and Rodrigues [2015] Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  16. Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for the multiple tsp with a fixed number of depots. INFORMS Journal on Computing 27(4), 636–645 (2015) Traub et al. [2022] Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  17. Traub, V., Vygen, J., Zenklusen, R.: Reducing path TSP to TSP. SIAM Journal on Computing 51(3), 20–24 (2022) Deppert et al. [2023] Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  18. Deppert, M., Kaul, M., Mnich, M.: A (3/2 + ε𝜀\varepsilonitalic_ε)-approximation for multiple TSP with a variable number of depots. In: Gørtz, I.L., Farach-Colton, M., Puglisi, S.J., Herman, G. (eds.) 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands. LIPIcs, vol. 274, pp. 39–13915 (2023) Chvatal [1979] Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  19. Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979) Hassin and Levin [2005] Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  20. Hassin, R., Levin, A.: A better-than-greedy approximation algorithm for the minimum set cover problem. SIAM Journal on Computing 35(1), 189–200 (2005) Gupta et al. [2023] Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  21. Gupta, A., Lee, E., Li, J.: A local search-based approach for set covering. In: SOSA 2023, pp. 1–11 (2023). SIAM Lai et al. [2023] Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  22. Lai, X., Xu, L., Xu, Z., Du, Y.: An approximation algorithm for k𝑘kitalic_k-depot split delivery vehicle routing problem. INFORMS Journal on Computing 35(5), 1179–1194 (2023) Heine et al. [2023] Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  23. Heine, F.C., Demleitner, A., Matuschke, J.: Bifactor approximation for location routing with vehicle and facility capacities. European Journal of Operational Research 304(2), 429–442 (2023) Zhao and Xiao [2023] Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  24. Zhao, J., Xiao, M.: Improved approximation algorithms for multidepot capacitated vehicle routing. In: COCOON 2023. Lecture Notes in Computer Science, vol. 14423, pp. 378–391 (2023) Dror and Trudeau [1990] Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  25. Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37(3), 383–402 (1990) Altinkemer and Gavish [1990] Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  26. Altinkemer, K., Gavish, B.: Heuristics for delivery problems with constant error guarantees. Transportation Science 24(4), 294–297 (1990) Williamson and Shmoys [2011] Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  27. Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, (2011) Yu and Liao [2021] Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer
  28. Yu, W., Liao, Y.: Approximation and polynomial algorithms for multi-depot capacitated arc routing problems. In: PDCAT 2021, pp. 93–100 (2021). Springer

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Authors (2)

  1. Jingyang Zhao 
  2. Mingyu Xiao 

Collections

Sign up for free to add this paper to one or more collections.

Sign Up

Tweets

Sign up for free to view the 1 tweet with 0 likes about this paper.

Sign Up for Free