Papers
Topics
Authors
Recent
Search
2000 character limit reached

Complexity Dichotomies for the Maximum Weighted Digraph Partition Problem

Published 3 Jul 2023 in cs.DM, cs.DS, cs.GT, and math.CO | (2307.01109v1)

Abstract: We introduce and study a new optimization problem on digraphs, termed Maximum Weighted Digraph Partition (MWDP) problem. We prove three complexity dichotomies for MWDP: on arbitrary digraphs, on oriented digraphs, and on symmetric digraphs. We demonstrate applications of the dichotomies for binary-action polymatrix games and several graph theory problems.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (29)
  1. Bounds on maximum weight directed cut. CoRR, abs/2304.10202, 2023.
  2. Coordination games on graphs. International Journal of Game Theory, 46(3):851–877, 2017.
  3. Coordination games on weighted directed graphs. Mathematics of Operations Research, 47(2):995–1025, 2022.
  4. J. Bang-Jensen and G. Z. Gutin. Basic terminology, notation and results. In J. Bang-Jensen and G. Z. Gutin, editors, Classes of Directed Graphs, Springer Monographs in Mathematics, pages 1–34. Springer, 2018.
  5. L. E. Blume. The statistical mechanics of strategic interaction. Games and Economic Behavior, 5(3):387 – 424, 1993.
  6. A. Bogomolnaia and M. O. Jackson. The stability of hedonic coalition structures. Games and Economic Behavior, 38(2):201–230, 2002.
  7. Settling the complexity of computing two-player Nash equilibria. Journal of the ACM, 56(3):14:1–14:57, 2009.
  8. Proper orientations and proper chromatic number. J. Combin. Th., Ser. B, 161:63–85, 2023.
  9. The complexity of computing a Nash equilibrium. SIAM J. Comput., 39(1):195–259, 2009.
  10. Complexity dichotomies for polymatrix games. in preparation, 2023.
  11. Complexity of efficient outcomes in binary-action polymatrix games and implications for coordination problems. In Proc. of IJCAI23. ACM, 2023.
  12. Pure-circuit: Strong inapproximability for PPAD. In Proc. of FOCS, pages 159–170. IEEE, 2022.
  13. Transductive label augmentation for improved deep network learning. In Proc. of ICPR, pages 1432–1437, 2018.
  14. G. Ellison. Learning, local interaction, and coordination. Econometrica, 61(5):1047–1071, 1993.
  15. A. Goldberg. Finding a maximum density subgraph, 1984. Technical Report UCB/CSD-84-171, EECS Department, Univ. California, Berkeley.
  16. E. B. Janovskaya. Equilibrium points in polymatrix games. (in Russian), Latvian Mathematical Journal, 1968.
  17. Graphical models for game theory. CoRR, abs/1301.2281, 2013.
  18. B. H. Korte and J. Vygen. Combinatorial optimization, volume 1. Springer, 2011.
  19. L. Lovász. Coverings and colorings of hypergraphs. Proc. 4th Southeastern Conference of Combinatorics, Graph Theory, and Computing, pages 3–12, 1973.
  20. S. Morris. Contagion. Review of Economic Studies, 67(1):57–78, January 2000.
  21. W. Nadara and M. Smulewicz. Decreasing the maximum average degree by deleting an independent set or a d𝑑ditalic_d-degenerate subgraph. Electron. J. Comb., 29(1), 2022. P 1.49.
  22. P. R. Neary. Competing conventions. Games and Economic Behavior, 76(1):301 – 328, 2012.
  23. P. R. Neary and J. Newton. Heterogeneity in preferences and behavior in threshold models. The Journal of Mechanism and Institution Design, 2(1):141–159, December 2017.
  24. M. Peski. Generalized risk-dominance and asymmetric dynamics. Journal of Economic Theory, 145(1):216–248, January 2010.
  25. J. Picard and M. Queyranne. A network flow solution to some nonlinear 0-1 programming problems, with applications to graph theory. Networks, 12(2):141–159, 1982.
  26. M. Rahn and G. Schäfer. Efficient equilibria in polymatrix coordination games. In Proc. of MFCS, pages 529–541. Springer, 2015.
  27. A. Rubinstein. Inapproximability of Nash equilibrium. SIAM J. Comput., 47(3):917–959, 2018.
  28. T. J. Schaefer. The complexity of satisfiability problems. In Proc. of STOC, pages 216–226. ACM, 1978.
  29. Protein function prediction as a graph-transduction game. Pattern Recognition Letters, 134:96–105, 2020.
Citations (3)
View on Semantic Scholar

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

Collections

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

Sign Up