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On group feedback Vertex Set parameterized by the size of the cutset

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Cygan, Marek, Pilipczuk, Marcin and Pilipczuk, Michał (2016) On group feedback Vertex Set parameterized by the size of the cutset. Algorithmica, 74 (2). pp. 630-642. doi:10.1007/s00453-014-9966-5 ISSN 0178-4617.

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Official URL: http://dx.doi.org/10.1007/s00453-014-9966-5

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Abstract

We study parameterized complexity of a generalization of the classical Feedback Vertex Set problem, namely the Group Feedback Vertex Set problem: we are given a graph G with edges labeled with group elements, and the goal is to compute the smallest set of vertices that hits all cycles of G that evaluate to a non-null element of the group. This problem generalizes not only Feedback Vertex Set, but also Subset Feedback Vertex Set, Multiway Cut and Odd Cycle Transversal . Completing the results of Guillemot (Discrete Optim 8(1):61–71, 2011), we provide a fixed-parameter algorithm for the parameterization by the size of the cutset only. Our algorithm works even if the group is given as a blackbox performing group operations.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions: Faculty of Science, Engineering and Medicine > Science > Computer Science
Library of Congress Subject Headings (LCSH): Computational complexity, Vertex operator algebras
Journal or Publication Title: Algorithmica
Publisher: Springer Verlag
ISSN: 0178-4617
Official Date: February 2016
Dates:
DateEvent
February 2016Published
25 December 2014Available
16 December 2013Accepted
Volume: 74
Number: 2
Page Range: pp. 630-642
DOI: 10.1007/s00453-014-9966-5
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 28 December 2015
Date of first compliant Open Access: 28 December 2015
Funder: Narodowe Centrum Nauki (NCN), Fundacja na rzecz Nauki Polskiej [Foundation for Polish Science] (FNP), European Research Council (ERC), Seventh Framework Programme (European Commission) (FP7)
Grant number: N206567140 (NCN), 267959 (MRC)
Embodied As: 1

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