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Alternative Parameterizations for Cluster Editing

  • Conference paper
SOFSEM 2011: Theory and Practice of Computer Science (SOFSEM 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6543))

Abstract

Given an undirected graph G and a nonnegative integer k, the NP-hard Cluster Editing problem asks whether G can be transformed into a disjoint union of cliques by applying at most k edge modifications. In the field of parameterized algorithmics, Cluster Editing has almost exclusively been studied parameterized by the solution size k. Contrastingly, in many real-world instances it can be observed that the parameter k is not really small. This observation motivates our investigation of parameterizations of Cluster Editing different from the solution size k. Our results are as follows. Cluster Editing is fixed-parameter tractable with respect to the parameter “size of a minimum cluster vertex deletion set of G”, a typically much smaller parameter than k. Cluster Editing remains NP-hard on graphs with maximum degree six. A restricted but practically relevant version of Cluster Editing is fixed-parameter tractable with respect to the combined parameter “number of clusters in the target graph” and “maximum number of modified edges incident to any vertex in G”. Many of our results also transfer to the NP-hard Cluster Deletion problem, where only edge deletions are allowed.

Supported by the DFG, research project PABI NI369/7.

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Authors and Affiliations

  1. Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, D-07743, Jena, Germany

    Christian Komusiewicz & Johannes Uhlmann

Authors
  1. Christian Komusiewicz
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  2. Johannes Uhlmann
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Editor information

Editors and Affiliations

  1. Ivana Černá, Department of Computer Science, Faculty of Informatics, Faculty of Informatics, Masaryk University, Botanicka 68 a, 602 00, Brno, Czech Republic

    Ivana Černá

  2. Department of Software Engineering, University of Szeged, Árpád tér 2., 6720, Szeged, Hungary

    Tibor Gyimóthy

  3. Informationstechnologie und Ausbildung, CAB F 16, F 13.1, Universitätstraße 6, ETH Zürich, 8092, Zürich, Switzerland

    Juraj Hromkovič

  4. School of History and Anthropology, Queen’s University, 15 University Square, BT7 1NN, Belfast, UK

    Keith Jefferey

  5. Department of Computer Science, Comenius University, 84248, Bratislava, Slovakia

    Rastislav Králović

  6. EURECOM, 2229 2229 Route des Crêtes, BP 193, 06904, Sophia Antipolis cedex, France

    Marko Vukolić

  7. Institute of Theoretical Computer Science, ETH Zürich, IFW E49.1, Haldeneggsteig 4, 8092, Zürich, Switzerland

    Stefan Wolf

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Komusiewicz, C., Uhlmann, J. (2011). Alternative Parameterizations for Cluster Editing. In: Černá, I., et al. SOFSEM 2011: Theory and Practice of Computer Science. SOFSEM 2011. Lecture Notes in Computer Science, vol 6543. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18381-2_29

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  • DOI: https://doi.org/10.1007/978-3-642-18381-2_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-18380-5

  • Online ISBN: 978-3-642-18381-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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