Generalized feedback vertex set problems on bounded-treewidth graphs: chordality is the key to single-exponential parameterised algorithms

Bonnet, Edouard, Brettell, Nick, Kwon, O-joung and Marx, Dániel (2018) Generalized feedback vertex set problems on bounded-treewidth graphs: chordality is the key to single-exponential parameterised algorithms. 12th International Symposium on Parameterized and Exact Computation (IPEC 2017). In: 12th International Symposium on Parameterized and Exact Computation (IPEC 2017), 06-08 Sept 2017, Vienna, Austria. ISBN 9783959770514. ISSN 1868-8969 [Conference or Workshop Item] (doi:10.4230/LIPIcs.IPEC.2017.7)

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Abstract

It has long been known that Feedback Vertex Set can be solved in time 2^O(w log w)n^O(1) on graphs of treewidth w, but it was only recently that this running time was improved to 2^O(w)n^O(1), that is, to single-exponential parameterized by treewidth. We investigate which generalizations of Feedback Vertex Set can be solved in a similar running time. Formally, for a class of graphs P, Bounded P-Block Vertex Deletion asks, given a graph G on n vertices and positive integers k and d, whether G contains a set S of at most k vertices such that each block of G-S has at most d vertices and is in P. Assuming that P is recognizable in polynomial time and satisfies a certain natural hereditary condition, we give a sharp characterization of when single-exponential parameterized algorithms are possible for fixed values of d: - if P consists only of chordal graphs, then the problem can be solved in time 2^O(wd^2) n^{O}(1), - if P contains a graph with an induced cycle of length ell>= 4, then the problem is not solvable in time 2^{o(w log w)} n^O(1)} even for fixed d=ell, unless the ETH fails. We also study a similar problem, called Bounded P-Component Vertex Deletion, where the target graphs have connected components of small size instead of having blocks of small size, and present analogous results.

Item Type: Conference or Workshop Item (Paper)
Additional Information: Article number = 7
Research Areas: A. > School of Science and Technology > Computer Science
Item ID: 24159
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Depositing User: Bade Ajibade
Date Deposited: 23 Apr 2018 13:41
Last Modified: 08 Feb 2021 18:34
URI: https://eprints.mdx.ac.uk/id/eprint/24159

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