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. In: 12th International Symposium on Parameterized and Exact Computation (IPEC 2017), 06-08 Sept 2017, Vienna, Austria.

[img]
Preview
PDF - Published version (with publisher's formatting)
Available under License Creative Commons Attribution.

Download (618kB) | Preview

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
Useful Links:
Depositing User: Bade Ajibade
Date Deposited: 23 Apr 2018 13:41
Last Modified: 08 Apr 2019 17:01
URI: https://eprints.mdx.ac.uk/id/eprint/24159

Actions (login required)

Edit Item Edit Item

Full text downloads (NB count will be zero if no full text documents are attached to the record)

Downloads per month over the past year