Fixed-parameter tractability for subset feedback set problems with parity constraints

Naonori Kakimura, Ken ichi Kawarabayashi

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The subset feedback set problem, which is a generalization of the well-known feedback vertex set problem, is that we are given an undirected graph G with a vertex subset S and a positive integer k, and the goal is to find a vertex set X of size at most k such that G-. X has no S-cycle, where an S-cycle is a cycle having at least one vertex of S. It was recently shown that this problem is fixed parameter tractable, where k is the parameter. In this paper, we further generalize this problem to one with the parity constraints, and show the fixed parameter tractability:. 1.For a parameter k, there exists a fixed-parameter algorithm that either finds a vertex set X of size k such that G-X has no S-cycle of even length, or concludes that such a vertex set does not exist.2.For a parameter k, there exists a fixed-parameter algorithm that either finds a vertex set X of size k such that G-X has no S-cycle of odd length, or concludes that such a vertex set does not exist.

Original languageEnglish
Pages (from-to)61-76
Number of pages16
JournalTheoretical Computer Science
Volume576
Issue number1
DOIs
Publication statusPublished - 2015
Externally publishedYes

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Keywords

  • Fixed-parameter algorithm
  • Graph minor theory
  • Parity constraints
  • Subset feedback set problem

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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