On group feedback vertex set parameterized by the size of the cutset

Authors:
Marek Cygan;Marcin Pilipczuk;Michał Pilipczuk
Affiliations:
IDSIA, University of Lugano, Switzerland;Institute of Informatics, University of Warsaw, Poland;Department of Informatics, University of Bergen, Norway
Venue:
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Year:
2012

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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 [Discr. Opt. 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.