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Algorithmica

pp 1–28 | Cite as

Mim-Width II. The Feedback Vertex Set Problem

  • Lars JaffkeEmail author
  • O-joung Kwon
  • Jan Arne Telle
Article
  • 18 Downloads

Abstract

We give a first polynomial-time algorithm for (Weighted) Feedback Vertex Set on graphs of bounded maximum induced matching width (mim-width). Explicitly, given a branch decomposition of mim-width w, we give an \(n^{\mathcal {O}(w)}\)-time algorithm that solves Feedback Vertex Set. This provides a unified polynomial-time algorithm for many well-known classes, such as Interval graphs, Permutation graphs, and Leaf power graphs (given a leaf root), and furthermore, it gives the first polynomial-time algorithms for other classes of bounded mim-width, such as Circular Permutation and Circular k-Trapezoid graphs (given a circular k-trapezoid model) for fixed k. We complement our result by showing that Feedback Vertex Set is \(\textsf {W}[1]\)-hard when parameterized by w and the hardness holds even when a linear branch decomposition of mim-width w is given.

Keywords

Graph width parameters Mim-width Graph classes Feedback vertex set 

Notes

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.Department of MathematicsIncheon National UniversityIncheonSouth Korea

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