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An Exact Algorithm for Subset Feedback Vertex Set on Chordal Graphs

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Parameterized and Exact Computation (IPEC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7535))

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Abstract

Given a graph G = (V,E) and a set S ⊆ V, a set U ⊆ V is a subset feedback vertex set of (G,S) if no cycle in G[V ∖ U] contains a vertex of S. The Subset Feedback Vertex Set problem takes as input G, S, and an integer k, and the question is whether (G,S) has a subset feedback vertex set of cardinality or weight at most k. Both the weighted and the unweighted versions of this problem are NP-complete on chordal graphs, even on their subclass split graphs. We give an algorithm with running time O(1.6708n) that enumerates all minimal subset feedback vertex sets on chordal graphs with n vertices. As a consequence, Subset Feedback Vertex Set can be solved in time O(1.6708n) on chordal graphs, both in the weighted and in the unweighted case. On arbitrary graphs, the fastest known algorithm for the problems has O(1.8638n) running time.

This work has been supported by the European Research Council, the Research Council of Norway, and the French National Research Agency.

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Author information

Authors and Affiliations

  1. Department of Informatics, University of Bergen, Norway

    Petr A. Golovach, Pinar Heggernes & Reza Saei

  2. LITA, Université de Lorraine - Metz, France

    Dieter Kratsch

Authors
  1. Petr A. Golovach
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  2. Pinar Heggernes
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  3. Dieter Kratsch
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  4. Reza Saei
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Editor information

Editors and Affiliations

  1. Department of Mathematics, National and Kapodistrian University of Athens, Panepistimioupolis, 15784, Athens, Greece

    Dimitrios M. Thilikos

  2. Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Gerhard J. Woeginger

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Golovach, P.A., Heggernes, P., Kratsch, D., Saei, R. (2012). An Exact Algorithm for Subset Feedback Vertex Set on Chordal Graphs. In: Thilikos, D.M., Woeginger, G.J. (eds) Parameterized and Exact Computation. IPEC 2012. Lecture Notes in Computer Science, vol 7535. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33293-7_10

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  • DOI: https://doi.org/10.1007/978-3-642-33293-7_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33292-0

  • Online ISBN: 978-3-642-33293-7

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