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Hitting forbidden subgraphs in graphs of bounded treewidth
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Cygan, Marek, Marx, Daniel, Pilipczuk, Marcin and Pilipczuk, Michał (2014) Hitting forbidden subgraphs in graphs of bounded treewidth. In: Csuhaj-Varjú, E. and Dietzfelbinger, Martin and Ésik, Zoltán, 1951-, (eds.) Mathematical foundations of computer science 2014 : proceedings, Part II 39th International Symposium, MFCS 2014, Budapest, Hungary, August 25-29, 2014. Lecture Notes in Computer Science (Volume 8635). Berlin ; London: Springer Verlag, pp. 189-200. ISBN 9783662444641
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Official URL: http://dx.doi.org/10.1007/978-3-662-44465-8_17
Abstract
We study the complexity of a generic hitting problem H -Subgraph Hitting , where given a fixed pattern graph H and an input graph G, we seek for the minimum size of a set X ⊆ V(G) that hits all subgraphs of G isomorphic to H. In the colorful variant of the problem, each vertex of G is precolored with some color from V(H) and we require to hit only H-subgraphs with matching colors. Standard techniques (e.g., Courcelle’s theorem) show that, for every fixed H and the problem is fixed-parameter tractable parameterized by the treewidth of G; however, it is not clear how exactly the running time should depend on treewidth. For the colorful variant, we demonstrate matching upper and lower bounds showing that the dependence of the running time on treewidth of G is tightly governed by μ(H), the maximum size of a minimal vertex separator in H. That is, we show for every fixed H that, on a graph of treewidth t, the colorful problem can be solved in time 2O(tμ(H))⋅|V(G)|, but cannot be solved in time 2o(tμ(H))⋅|V(G)|O(1), assuming the Exponential Time Hypothesis (ETH). Furthermore, we give some preliminary results showing that, in the absence of colors, the parameterized complexity landscape of H -Subgraph Hitting is much richer.
| Item Type: | Book Item | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software | ||||
| Divisions: | Faculty of Science > Computer Science | ||||
| Library of Congress Subject Headings (LCSH): | Graph theory, Computational complexity | ||||
| Series Name: | Lecture Notes in Computer Science | ||||
| Publisher: | Springer Verlag | ||||
| Place of Publication: | Berlin ; London | ||||
| ISBN: | 9783662444641 | ||||
| ISSN: | 0302-9743 | ||||
| Book Title: | Mathematical foundations of computer science 2014 : proceedings, Part II 39th International Symposium, MFCS 2014, Budapest, Hungary, August 25-29, 2014 | ||||
| Editor: | Csuhaj-Varjú, E. and Dietzfelbinger, Martin and Ésik, Zoltán, 1951- | ||||
| Official Date: | 2014 | ||||
| Dates: |
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| Number: | Volume 8635 | ||||
| Number of Pages: | 12 | ||||
| Page Range: | pp. 189-200 | ||||
| DOI: | 10.1007/978-3-662-44465-8_17 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Description: | |||||
| Funder: | Seventh Framework Programme (European Commission) (FP7), European Research Council (ERC), Országos Tudományos Kutatási Alapprogramok (OTKA), Narodowe Centrum Nauki (NCN) | ||||
| Grant number: | 267959 (ERC), 280152 (ERC), NK10564 (OTKA), DEC-2012/05/D/ST6/03214 (NCN) |
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