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Enumerating Minimal Subset Feedback Vertex Sets

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Abstract

The Subset Feedback Vertex Set problem takes as input a pair (G,S), where G=(V,E) is a graph with weights on its vertices, and S⊆V. The task is to find a set of vertices of total minimum weight to be removed from G, such that in the remaining graph no cycle contains a vertex of S. We show that this problem can be solved in time O(1.8638n), where n=|V|. This is a consequence of the main result of this paper, namely that all minimal subset feedback vertex sets of a graph can be enumerated in time O(1.8638n).

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Acknowledgements

The authors would like to thank the anonymous referees whose valuable suggestions helped improve the presentation of the paper.

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Authors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Fedor V. Fomin, Pinar Heggernes & Yngve Villanger

  2. LITA, Université Paul Verlaine, Metz, France

    Dieter Kratsch

  3. Department of Mathematics, University of Ioannina, Ioannina, Greece

    Charis Papadopoulos

Authors
  1. Fedor V. Fomin
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  2. Pinar Heggernes
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  3. Dieter Kratsch
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  4. Charis Papadopoulos
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  5. Yngve Villanger
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Corresponding author

Correspondence to Charis Papadopoulos.

Additional information

This work is supported by the Research Council of Norway. A preliminary version of this work was presented at WADS 2011 [8].

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Fomin, F.V., Heggernes, P., Kratsch, D. et al. Enumerating Minimal Subset Feedback Vertex Sets. Algorithmica 69, 216–231 (2014). https://doi.org/10.1007/s00453-012-9731-6

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  • DOI: https://doi.org/10.1007/s00453-012-9731-6

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