Approximability of the independent feedback vertex set problem for bipartite graphs

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Abstract

Given an undirected graph G with n vertices, the independent feedback vertex set problem is to find a vertex subset F of G with the minimum number of vertices such that F is both an independent set and a feedback vertex set of G, if it exists. This problem is known to be NP-hard for bipartite planar graphs of maximum degree four. In this paper, we study the approximability of the problem. We first show that, for any fixed ε>0, unless P=NP, there exists no polynomial-time n1−ε-approximation algorithm even for bipartite planar graphs. We then give an α(Δ−1)/2-approximation algorithm for bipartite graphs G of maximum degree Δ, which runs in t(α,G)+O(Δn) time, under the assumption that there is an α-approximation algorithm for the original feedback vertex set problem on bipartite graphs which runs in t(α,G) time. This algorithmic result also yields a polynomial-time (exact) algorithm for the independent feedback vertex set problem on bipartite graphs of maximum degree three.

Original languageEnglish
Pages (from-to)227-236
Number of pages10
JournalTheoretical Computer Science
Volume849
DOIs
Publication statusPublished - 2021 Jan 6

Keywords

  • Bipartite graphs
  • Graph algorithms
  • Inapproximability
  • Independent feedback vertex set

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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