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Deterministic Algorithms for the Independent Feedback Vertex Set Problem

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Combinatorial Algorithms (IWOCA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8986))

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  • International Workshop on Combinatorial Algorithms

Abstract

A feedback vertex set F of an undirected graph G is a vertex subset of G whose removal results in a forest. Such a set F is said to be independent if F forms an independent set of G. In this paper, we study the problem of finding an independent feedback vertex set of a given graph with the minimum number of vertices, from the viewpoint of graph classes. This problem is NP-hard even for planar bipartite graphs of maximum degree four. However, we show that the problem is solvable in linear time for graphs having tree-like structures, more specifically, for bounded treewidth graphs, chordal graphs and cographs. We then give a fixed-parameter algorithm for planar graphs when parameterized by the solution size. Such a fixed-parameter algorithm is already known for general graphs, but our algorithm is exponentially faster than the known one.

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Acknowledgments

We are grateful to Saket Saurabh for fruitful discussions with him. This work is partially supported by JSPS KAKENHI Grant Numbers 25106504 and 25330003.

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Authors and Affiliations

  1. Graduate School of Information Sciences, Tohoku University, Aoba-yama 6-6-05, Sendai, 980-8579, Japan

    Yuma Tamura, Takehiro Ito & Xiao Zhou

  2. JST, ERATO, Kawarabayashi Large Graph Project, c/o Global Research Center for Big Data Mathematics, NII, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, 101-8430, Japan

    Yuma Tamura

Authors
  1. Yuma Tamura
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  2. Takehiro Ito
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  3. Xiao Zhou
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Corresponding author

Correspondence to Yuma Tamura .

Editor information

Editors and Affiliations

  1. Faculty of Mathematics and Physics, Charles University, Praha, Czech Republic

    Kratochvíl Jan

  2. University of Newcastle, Newcastle, New South Wales, Australia

    Mirka Miller

  3. University of Minnesota, Duluth Department of Mathematics, Duluth, Minnesota, USA

    Dalibor Froncek

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Tamura, Y., Ito, T., Zhou, X. (2015). Deterministic Algorithms for the Independent Feedback Vertex Set Problem. In: Jan, K., Miller, M., Froncek, D. (eds) Combinatorial Algorithms. IWOCA 2014. Lecture Notes in Computer Science(), vol 8986. Springer, Cham. https://doi.org/10.1007/978-3-319-19315-1_31

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  • DOI: https://doi.org/10.1007/978-3-319-19315-1_31

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19314-4

  • Online ISBN: 978-3-319-19315-1

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