2000 character limit reached
How to apply tree decomposition ideas in large networks?
Published 19 Dec 2023 in cs.DM | (2312.12354v1)
Abstract: Graph decompositions are the natural generalisation of tree decompositions where the decomposition tree is replaced by a genuine graph. Recently they found theoretical applications in the theory of sparsity, topological graph theory, structural graph theory and geometric group theory. We demonstrate applicability of graph decompositions on large networks by implementing an efficient algorithm and testing it on road networks.
- Tree-like structure in large social and information networks. In 2013 IEEE 13th International Conference on Data Mining, pages 1–10. IEEE, 2013.
- Hans L Bodlaender. A partial k-arboretum of graphs with bounded treewidth. Theoretical computer science, 209(1-2):1–45, 1998.
- Large independent sets from local considerations. Combinatorica, pages 1–42, 2023.
- Johannes Carmesin. A Whitney type theorem for surfaces: characterising graphs with locally planar embeddings. Preprint, available at http://web.mat.bham.ac.uk/J.Carmesin/.
- Johannes Carmesin. Local 2-separators. Journal of Combinatorial Theory, Series B, 156:101–144, 2022.
- The structure of graphs without cycles of intermediate length. In preparation.
- Towards a Stallings type theorem for finite groups. In preparation.
- Bruno Courcelle. The monadic second-order logic of graphs. I. recognizable sets of finite graphs. Information and computation, 85(1):12–75, 1990.
- Graph structure and monadic second-order logic: a language-theoretic approach, volume 138. Cambridge University Press, 2012.
- Canonical graph decompositions via coverings. arXiv preprint arXiv:2207.04855, 2022.
- Graph minor hierarchies. Discrete Applied Mathematics, 145(2):167–182, 2005.
- Tangles and the Mona Lisa. arXiv preprint arXiv:1603.06652, 2016.
- Santo Fortunato. Community detection in graphs. Physics reports, 486(3-5):75–174, 2010.
- Local algorithms, regular graphs of large girth, and random regular graphs. Combinatorica, 38(3):619–664, 2018.
- Community detection in networks: A multidisciplinary review. Journal of Network and Computer Applications, 108:87–111, 2018.
- Richard M Karp. Reducibility among combinatorial problems. In Complexity of computer computations, pages 85–103. Springer, 1972.
- Clustering with tangles: Algorithmic framework and theoretical guarantees. Journal of Machine Learning Research, 24(190):1–56, 2023.
- Large independent sets in regular graphs of large girth. Journal of Combinatorial Theory, Series B, 97(6):999–1009, 2007.
- James MacQueen et al. Some methods for classification and analysis of multivariate observations. In Proceedings of the fifth Berkeley symposium on mathematical statistics and probability, volume 1, pages 281–297. Oakland, CA, USA, 1967.
- Jaroslav Nešetřil and Patrice Ossona de Mendez. Sparsity: graphs, structures, and algorithms. Springer, 2012.
- Finding and evaluating community structure in networks. Physical review E, 69(2):026113, 2004.
- OpenStreetMap contributors. OpenStreetMap . https://www.openstreetmap.org, 2023.
- Graph minors. X. Obstructions to tree-decompositions. J. Combin. Theory, Series B, 52:153–190, 1991.
- Maps of random walks on complex networks reveal community structure. Proceedings of the national academy of sciences, 105(4):1118–1123, 2008.
- Ulrike Von Luxburg. A tutorial on spectral clustering. Statistics and computing, 17(4):395–416, 2007.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.