English

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

Data Structures and Algorithms 2011-12-30 v1

Abstract

We study the parameterized complexity of a robust 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 polynomial-time oracle.

Keywords

Cite

@article{arxiv.1112.6255,
  title  = {On group feedback vertex set parameterized by the size of the cutset},
  author = {Marek Cygan and Marcin Pilipczuk and Michał Pilipczuk},
  journal= {arXiv preprint arXiv:1112.6255},
  year   = {2011}
}