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A Fast Branching Algorithm for Cluster Vertex Deletion

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Computer Science - Theory and Applications (CSR 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8476))

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Abstract

In the family of clustering problems we are given a set of objects (vertices of the graph), together with some observed pairwise similarities (edges). The goal is to identify clusters of similar objects by slightly modifying the graph to obtain a cluster graph (disjoint union of cliques).

Hüffner et al. [LATIN 2008, Theory Comput. Syst. 2010] initiated the parameterized study of Cluster Vertex Deletion, where the allowed modification is vertex deletion, and presented an elegant \(\mathcal{O}(2^k k^9 + nm)\)-time fixed-parameter algorithm, parameterized by the solution size. In the last 5 years, this algorithm remained the fastest known algorithm for Cluster Vertex Deletion and, thanks to its simplicity, became one of the textbook examples of an application of the iterative compression principle. In our work we break the 2k-barrier for Cluster Vertex Deletion and present an \(\mathcal{O}(1.9102^k (n+m))\)-time branching algorithm.

Partially supported by NCN grant N206567140 and Foundation for Polish Science.

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Author information

Authors and Affiliations

  1. Chennai Mathematical Institute, Chennai, India

    Anudhyan Boral

  2. Institute of Informatics, University of Warsaw, Poland

    Marek Cygan & Tomasz Kociumaka

  3. Department of Informatics, University of Bergen, Norway

    Marcin Pilipczuk

Authors
  1. Anudhyan Boral
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  2. Marek Cygan
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  3. Tomasz Kociumaka
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  4. Marcin Pilipczuk
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Editor information

Editors and Affiliations

  1. Steklov Institute of Mathematics at St. Petersburg, Russian Academy of Sciences, 27 Fontanka,, 191023, St. Petersburg, Russia

    Edward A. Hirsch

  2. Higher School of Economics, National Research University, 109028, Moscow, Russia

    Sergei O. Kuznetsov

  3. CNRS and University Paris Diderot, Paris, France

    Jean-Éric Pin

  4. Moscow State University, 119992, Moscow, Russia

    Nikolay K. Vereshchagin

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Boral, A., Cygan, M., Kociumaka, T., Pilipczuk, M. (2014). A Fast Branching Algorithm for Cluster Vertex Deletion. In: Hirsch, E.A., Kuznetsov, S.O., Pin, JÉ., Vereshchagin, N.K. (eds) Computer Science - Theory and Applications. CSR 2014. Lecture Notes in Computer Science, vol 8476. Springer, Cham. https://doi.org/10.1007/978-3-319-06686-8_9

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  • DOI: https://doi.org/10.1007/978-3-319-06686-8_9

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06685-1

  • Online ISBN: 978-3-319-06686-8

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