A single exponential-time FPT algorithm for cactus contraction
For a collection F of graphs, the F-Contraction problem takes a graph G and an integer k as input and decides if G can be modified to some graph in F using at most k edge contractions. The F-Contraction problem is NP-Complete for several graph classes F. Heggernes et al. (2014) [4] initiated the stu...
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| Published in: | Theoretical computer science Vol. 954; p. 113803 |
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| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
18.04.2023
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| ISSN: | 0304-3975, 1879-2294 |
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| Abstract | For a collection F of graphs, the F-Contraction problem takes a graph G and an integer k as input and decides if G can be modified to some graph in F using at most k edge contractions. The F-Contraction problem is NP-Complete for several graph classes F. Heggernes et al. (2014) [4] initiated the study of F-Contraction in the realm of parameterized complexity. They showed that it is FPT if F is the set of all trees or the set of all paths. In this paper, we study F-Contraction where F is the set of all cactus graphs and show that we can solve it in 2O(k)⋅|V(G)|O(1) time. |
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| AbstractList | For a collection F of graphs, the F-Contraction problem takes a graph G and an integer k as input and decides if G can be modified to some graph in F using at most k edge contractions. The F-Contraction problem is NP-Complete for several graph classes F. Heggernes et al. (2014) [4] initiated the study of F-Contraction in the realm of parameterized complexity. They showed that it is FPT if F is the set of all trees or the set of all paths. In this paper, we study F-Contraction where F is the set of all cactus graphs and show that we can solve it in 2O(k)⋅|V(G)|O(1) time. |
| ArticleNumber | 113803 |
| Author | Tale, Prafullkumar Krithika, R. Misra, Pranabendu |
| Author_xml | – sequence: 1 givenname: R. surname: Krithika fullname: Krithika, R. email: krithika@iitpkd.ac.in organization: Indian Institute of Technology Palakkad, Palakkad, India – sequence: 2 givenname: Pranabendu surname: Misra fullname: Misra, Pranabendu email: pranabendu@cmi.ac.in organization: Chennai Mathematical Institute, Chennai, India – sequence: 3 givenname: Prafullkumar surname: Tale fullname: Tale, Prafullkumar email: prafullkumar@iiserpune.ac.in organization: Indian Institute of Science, Education and Research Pune, Pune, India |
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| Cites_doi | 10.1016/j.tcs.2013.02.030 10.1007/s00453-012-9630-x 10.1016/j.jctb.2014.09.002 10.1007/s00236-014-0204-z 10.1007/s00224-018-9892-z 10.1145/3319909 10.1016/0166-218X(81)90039-1 10.1016/0166-218X(83)90101-4 10.1016/j.ipl.2013.09.004 10.1016/0022-0000(83)90012-0 10.1016/j.tcs.2012.12.041 10.1007/s00453-021-00897-6 10.1137/130907392 10.1007/s00453-012-9670-2 |
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| References | Watanabe, Ae, Nakamura (br0020) 1983; 6 Martin, Paulusma (br0120) 2015; 111 Golovach, van't Hof, Paulusma (br0090) 2013; 476 Cygan, Fomin, Kowalik, Lokshtanov, Marx, Pilipczuk, Pilipczuk, Saurabh (br0190) 2015 Watanabe, Ae, Nakamura (br0010) 1981; 3 Fomin, Lokshtanov, Saurabh, Zehavi (br0200) 2019 Nederlof (br0210) 2013; 65 Krithika, Misra, Rai, Tale (br0180) 2016 Agarwal, Saurabh, Tale (br0050) 2019; 63 Naor, Schulman, Srinivasan (br0220) 1995 Guillemot, Marx (br0070) 2013; 113 Heggernes, Hof, Lokshtanov, Paul (br0080) 2013; 27 Agrawal, Lokshtanov, Saurabh, Zehavi (br0160) 2019; 11 Cai, Guo (br0110) 2013 Belmonte, Golovach, Hof, Paulusma (br0130) 2014; 51 Golovach, Kamiński, Paulusma, Thilikos (br0140) 2013; 481 Asano, Hirata (br0030) 1983; 26 Lokshtanov, Misra, Saurabh (br0170) 2013 Agrawal, Kanesh, Saurabh, Tale (br0060) 2017 Heggernes, van't Hof, Lévêque, Lokshtanov, Paul (br0040) 2014; 68 Saurabh, Souza, Tale (br0100) 2020 Saurabh, Tale (br0150) 2022; 84 Belmonte (10.1016/j.tcs.2023.113803_br0130) 2014; 51 Golovach (10.1016/j.tcs.2023.113803_br0140) 2013; 481 Martin (10.1016/j.tcs.2023.113803_br0120) 2015; 111 Lokshtanov (10.1016/j.tcs.2023.113803_br0170) 2013 Saurabh (10.1016/j.tcs.2023.113803_br0150) 2022; 84 Nederlof (10.1016/j.tcs.2023.113803_br0210) 2013; 65 Krithika (10.1016/j.tcs.2023.113803_br0180) 2016 Heggernes (10.1016/j.tcs.2023.113803_br0080) 2013; 27 Cygan (10.1016/j.tcs.2023.113803_br0190) 2015 Guillemot (10.1016/j.tcs.2023.113803_br0070) 2013; 113 Saurabh (10.1016/j.tcs.2023.113803_br0100) 2020 Cai (10.1016/j.tcs.2023.113803_br0110) 2013 Agarwal (10.1016/j.tcs.2023.113803_br0050) 2019; 63 Asano (10.1016/j.tcs.2023.113803_br0030) 1983; 26 Agrawal (10.1016/j.tcs.2023.113803_br0160) 2019; 11 Fomin (10.1016/j.tcs.2023.113803_br0200) 2019 Heggernes (10.1016/j.tcs.2023.113803_br0040) 2014; 68 Watanabe (10.1016/j.tcs.2023.113803_br0010) 1981; 3 Agrawal (10.1016/j.tcs.2023.113803_br0060) 2017 Golovach (10.1016/j.tcs.2023.113803_br0090) 2013; 476 Watanabe (10.1016/j.tcs.2023.113803_br0020) 1983; 6 Naor (10.1016/j.tcs.2023.113803_br0220) 1995 |
| References_xml | – start-page: 182 year: 1995 end-page: 191 ident: br0220 article-title: Splitters and near-optimal derandomization publication-title: 36th Annual Symposium on Foundations of Computer Science – start-page: 243 year: 2013 end-page: 254 ident: br0170 article-title: On the hardness of eliminating small induced subgraphs by contracting edges publication-title: International Symposium on Parameterized and Exact Computation – volume: 6 start-page: 63 year: 1983 end-page: 78 ident: br0020 article-title: On the NP-hardness of edge-deletion and edge-contraction problems publication-title: Discrete Appl. Math. – volume: 27 start-page: 2143 year: 2013 end-page: 2156 ident: br0080 article-title: Obtaining a bipartite graph by contracting few edges publication-title: SIAM J. Discrete Math. – volume: 11 start-page: 1 year: 2019 end-page: 22 ident: br0160 article-title: Split contraction: the untold story publication-title: ACM Trans. Comput. Theory – year: 2016 ident: br0180 article-title: Lossy kernels for graph contraction problems publication-title: 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS) – volume: 3 year: 1981 ident: br0010 article-title: On the removal of forbidden graphs by edge-deletion or by edge-contraction publication-title: Discrete Appl. Math. – volume: 63 start-page: 587 year: 2019 end-page: 614 ident: br0050 article-title: On the parameterized complexity of contraction to generalization of trees publication-title: Theory Comput. Syst. – volume: 111 start-page: 17 year: 2015 end-page: 37 ident: br0120 article-title: The computational complexity of disconnected cut and 2k2-partition publication-title: J. Comb. Theory, Ser. B – volume: 113 start-page: 906 year: 2013 end-page: 912 ident: br0070 article-title: A faster FPT algorithm for bipartite contraction publication-title: Inf. Process. Lett. – volume: 476 start-page: 38 year: 2013 end-page: 46 ident: br0090 article-title: Obtaining planarity by contracting few edges publication-title: Theor. Comput. Sci. – volume: 68 start-page: 109 year: 2014 end-page: 132 ident: br0040 article-title: Contracting graphs to paths and trees publication-title: Algorithmica – year: 2015 ident: br0190 article-title: Parameterized Algorithms – start-page: 97 year: 2013 end-page: 109 ident: br0110 article-title: Contracting few edges to remove forbidden induced subgraphs publication-title: IPEC – year: 2019 ident: br0200 article-title: Kernelization: Theory of Parameterized Preprocessing – volume: 65 start-page: 868 year: 2013 end-page: 884 ident: br0210 article-title: Fast polynomial-space algorithms using inclusion-exclusion publication-title: Algorithmica – start-page: 31 year: 2017 end-page: 42 ident: br0060 article-title: Paths to trees and cacti publication-title: International Conference on Algorithms and Complexity – volume: 26 start-page: 197 year: 1983 end-page: 208 ident: br0030 article-title: Edge-contraction problems publication-title: J. Comput. Syst. Sci. – volume: 51 start-page: 473 year: 2014 end-page: 497 ident: br0130 article-title: Parameterized complexity of three edge contraction problems with degree constraints publication-title: Acta Inform. – volume: 84 start-page: 405 year: 2022 end-page: 435 ident: br0150 article-title: On the parameterized complexity of maximum degree contraction problem publication-title: Algorithmica – volume: 481 start-page: 74 year: 2013 end-page: 84 ident: br0140 article-title: Increasing the minimum degree of a graph by contractions publication-title: Theor. Comput. Sci. – year: 2020 ident: br0100 article-title: On the parameterized complexity of grid contraction publication-title: 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020) – volume: 481 start-page: 74 year: 2013 ident: 10.1016/j.tcs.2023.113803_br0140 article-title: Increasing the minimum degree of a graph by contractions publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2013.02.030 – year: 2019 ident: 10.1016/j.tcs.2023.113803_br0200 – volume: 65 start-page: 868 issue: 4 year: 2013 ident: 10.1016/j.tcs.2023.113803_br0210 article-title: Fast polynomial-space algorithms using inclusion-exclusion publication-title: Algorithmica doi: 10.1007/s00453-012-9630-x – start-page: 31 year: 2017 ident: 10.1016/j.tcs.2023.113803_br0060 article-title: Paths to trees and cacti – volume: 111 start-page: 17 year: 2015 ident: 10.1016/j.tcs.2023.113803_br0120 article-title: The computational complexity of disconnected cut and 2k2-partition publication-title: J. Comb. Theory, Ser. B doi: 10.1016/j.jctb.2014.09.002 – volume: 51 start-page: 473 issue: 7 year: 2014 ident: 10.1016/j.tcs.2023.113803_br0130 article-title: Parameterized complexity of three edge contraction problems with degree constraints publication-title: Acta Inform. doi: 10.1007/s00236-014-0204-z – year: 2015 ident: 10.1016/j.tcs.2023.113803_br0190 – volume: 63 start-page: 587 issue: 3 year: 2019 ident: 10.1016/j.tcs.2023.113803_br0050 article-title: On the parameterized complexity of contraction to generalization of trees publication-title: Theory Comput. Syst. doi: 10.1007/s00224-018-9892-z – volume: 11 start-page: 1 issue: 3 year: 2019 ident: 10.1016/j.tcs.2023.113803_br0160 article-title: Split contraction: the untold story publication-title: ACM Trans. Comput. Theory doi: 10.1145/3319909 – volume: 3 issue: 2 year: 1981 ident: 10.1016/j.tcs.2023.113803_br0010 article-title: On the removal of forbidden graphs by edge-deletion or by edge-contraction publication-title: Discrete Appl. Math. doi: 10.1016/0166-218X(81)90039-1 – start-page: 182 year: 1995 ident: 10.1016/j.tcs.2023.113803_br0220 article-title: Splitters and near-optimal derandomization – volume: 6 start-page: 63 issue: 1 year: 1983 ident: 10.1016/j.tcs.2023.113803_br0020 article-title: On the NP-hardness of edge-deletion and edge-contraction problems publication-title: Discrete Appl. Math. doi: 10.1016/0166-218X(83)90101-4 – volume: 113 start-page: 906 issue: 22–24 year: 2013 ident: 10.1016/j.tcs.2023.113803_br0070 article-title: A faster FPT algorithm for bipartite contraction publication-title: Inf. Process. Lett. doi: 10.1016/j.ipl.2013.09.004 – year: 2016 ident: 10.1016/j.tcs.2023.113803_br0180 article-title: Lossy kernels for graph contraction problems – year: 2020 ident: 10.1016/j.tcs.2023.113803_br0100 article-title: On the parameterized complexity of grid contraction – volume: 26 start-page: 197 issue: 2 year: 1983 ident: 10.1016/j.tcs.2023.113803_br0030 article-title: Edge-contraction problems publication-title: J. Comput. Syst. Sci. doi: 10.1016/0022-0000(83)90012-0 – volume: 476 start-page: 38 year: 2013 ident: 10.1016/j.tcs.2023.113803_br0090 article-title: Obtaining planarity by contracting few edges publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2012.12.041 – start-page: 97 year: 2013 ident: 10.1016/j.tcs.2023.113803_br0110 article-title: Contracting few edges to remove forbidden induced subgraphs – volume: 84 start-page: 405 issue: 2 year: 2022 ident: 10.1016/j.tcs.2023.113803_br0150 article-title: On the parameterized complexity of maximum degree contraction problem publication-title: Algorithmica doi: 10.1007/s00453-021-00897-6 – volume: 27 start-page: 2143 issue: 4 year: 2013 ident: 10.1016/j.tcs.2023.113803_br0080 article-title: Obtaining a bipartite graph by contracting few edges publication-title: SIAM J. Discrete Math. doi: 10.1137/130907392 – start-page: 243 year: 2013 ident: 10.1016/j.tcs.2023.113803_br0170 article-title: On the hardness of eliminating small induced subgraphs by contracting edges – volume: 68 start-page: 109 issue: 1 year: 2014 ident: 10.1016/j.tcs.2023.113803_br0040 article-title: Contracting graphs to paths and trees publication-title: Algorithmica doi: 10.1007/s00453-012-9670-2 |
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| SubjectTerms | Cactus graphs Fixed parameter tractable algorithms Graph contraction |
| Title | A single exponential-time FPT algorithm for cactus contraction |
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