Generalized feedback vertex set problems on boundedtreewidth graphs: chordality is the key to singleexponential parameterised algorithms
Bonnet, Edouard, Brettell, Nick, Kwon, Ojoung and Marx, Dániel (2018) Generalized feedback vertex set problems on boundedtreewidth graphs: chordality is the key to singleexponential parameterised algorithms. 12th International Symposium on Parameterized and Exact Computation (IPEC 2017). In: 12th International Symposium on Parameterized and Exact Computation (IPEC 2017), 0608 Sept 2017, Vienna, Austria. ISBN 9783959770514. ISSN 18688969 [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 singleexponential 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 PBlock 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 GS 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 singleexponential 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 PComponent 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:  09 Jun 2021 17:20 
URI:  https://eprints.mdx.ac.uk/id/eprint/24159 
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