LIPIcs.IPEC.2024.13.pdf
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Kick the Cliques
Authors
Gaétan Berthe 
,
Marin Bougeret ,
Daniel Gonçalves ,
Jean-Florent Raymond
-
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Volume:
19th International Symposium on Parameterized and Exact Computation (IPEC 2024)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Symposium on Parameterized and Exact Computation (IPEC) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-12-05
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Gaétan Berthe, Marin Bougeret, Daniel Gonçalves, and Jean-Florent Raymond. Kick the Cliques. In 19th International Symposium on Parameterized and Exact Computation (IPEC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 321, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.IPEC.2024.13
Abstract
In the K_r-Hitting problem, given a graph G and an integer k one has to decide if there exists a set of at most k vertices whose removal destroys all r-cliques of G.
In this paper we give an algorithm for K_r-Hitting that runs in subexponential FPT time on graph classes satisfying two simple conditions related to cliques and treewidth. As an application we show that our algorithm solves K_r-Hitting in time
- 2^{O_r(k^{(r+1)/(r+2)}log k)} ⋅ n^{O_r(1)} in pseudo-disk graphs and map-graphs;
- 2^{O_{t,r}(k^{2/3}log k)} ⋅ n^{O_r(1)} in K_{t,t}-subgraph-free string graphs; and
- 2^{O_{H,r}(k^{2/3}log k)} ⋅ n^{O_r(1)} in H-minor-free graphs.
Subject Classification
ACM Subject Classification
- Mathematics of computing → Graph algorithms
- Theory of computation → Fixed parameter tractability
- Theory of computation → Computational geometry
Keywords
- Subexponential FPT algorithms
- implicit hitting set problems
- geometric intersection graphs
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References
- Noga Alon, Paul Seymour, and Robin Thomas. A separator theorem for nonplanar graphs. Journal of the American Mathematical Society, 3(4):801-808, 1990. URL: http://www.jstor.org/stable/1990903.
- Shinwoo An, Kyungjin Cho, and Eunjin Oh. Faster algorithms for cycle hitting problems on disk graphs. In Pat Morin and Subhash Suri, editors, Algorithms and Data Structures - 18th International Symposium, WADS 2023, Montreal, QC, Canada, July 31 - August 2, 2023, Proceedings, volume 14079 of Lecture Notes in Computer Science, pages 29-42, Berlin, Heidelberg, 2023. Springer. URL: https://doi.org/10.1007/978-3-031-38906-1_3.
-
Gaétan Berthe, Marin Bougeret, Daniel Gonçalves, and Jean-Florent Raymond. FVS for pseudo-disk graphs in subexponential FPT time. In Proceedings of WG 2024. LNCS, Springer, 2024.
- Gaétan Berthe, Marin Bougeret, Daniel Gonçalves, and Jean-Florent Raymond. Subexponential Algorithms in Geometric Graphs via the Subquadratic Grid Minor Property: The Role of Local Radius. In Hans L. Bodlaender, editor, 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024), volume 294 of Leibniz International Proceedings in Informatics (LIPIcs), pages 11:1-11:18, Dagstuhl, Germany, 2024. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.SWAT.2024.11.
- Zhi-Zhong Chen, Michelangelo Grigni, and Christos H Papadimitriou. Map graphs. Journal of the ACM (JACM), 49(2):127-138, 2002. URL: https://doi.org/10.1145/506147.506148.
- Norishige Chiba and Takao Nishizeki. Arboricity and subgraph listing algorithms. SIAM Journal on computing, 14(1):210-223, 1985. URL: https://doi.org/10.1137/0214017.
- Erik D Demaine, Fedor V Fomin, Mohammadtaghi Hajiaghayi, and Dimitrios M Thilikos. Subexponential parameterized algorithms on bounded-genus graphs and h-minor-free graphs. Journal of the ACM (JACM), 52(6):866-893, 2005. URL: https://doi.org/10.1145/1101821.1101823.
- Zdeněk Dvořák and Sergey Norin. Treewidth of graphs with balanced separations. J. Comb. Theory B, 137:137-144, 2019. URL: https://doi.org/10.1016/j.jctb.2018.12.007.
- Fedor V Fomin, Daniel Lokshtanov, Venkatesh Raman, and Saket Saurabh. Bidimensionality and EPTAS. In Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms, pages 748-759. SIAM, 2011. URL: https://doi.org/10.1137/1.9781611973082.59.
- Russell Impagliazzo and Ramamohan Paturi. On the complexity of k-sat. Journal of Computer and System Sciences, 62(2):367-375, 2001. URL: https://doi.org/10.1006/jcss.2000.1727.
-
A Kostochka. On the minimum of the Hadwiger number for graphs with given average degree. Metody Diskret. Analiz., 38:37-58, 1982. English translation: AMS Translations (2), 132:15-32, 1986.
- James R. Lee. Separators in Region Intersection Graphs. In Christos H. Papadimitriou, editor, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017), volume 67 of Leibniz International Proceedings in Informatics (LIPIcs), pages 1:1-1:8, Dagstuhl, Germany, 2017. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.ITCS.2017.1.
- John M. Lewis and Mihalis Yannakakis. The node-deletion problem for hereditary properties is np-complete. J. Comput. Syst. Sci., 20(2):219-230, 1980. URL: https://doi.org/10.1016/0022-0000(80)90060-4.
- Daniel Lokshtanov, Fahad Panolan, Saket Saurabh, Jie Xue, and Meirav Zehavi. Subexponential parameterized algorithms on disk graphs (extended abstract). In Proceedings of the 2022 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 2005-2031. SIAM, 2022. Full version available at https://sites.cs.ucsb.edu/~daniello/papers/subexpDiskOCTandFriends.pdf. URL: https://doi.org/10.1137/1.9781611977073.80.
-
Andrew Thomason. An extremal function for contractions of graphs. In Mathematical Proceedings of the Cambridge Philosophical Society, volume 95(2), pages 261-265. Cambridge University Press, 1984.
- David R Wood. On the maximum number of cliques in a graph. Graphs and Combinatorics, 23(3):337-352, 2007. URL: https://doi.org/10.1007/s00373-007-0738-8.