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On the NP-Completeness of Some Graph Cluster Measures

  • Conference paper
SOFSEM 2006: Theory and Practice of Computer Science (SOFSEM 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3831))

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Abstract

Graph clustering is the problem of identifying sparsely connected dense subgraphs (clusters) in a given graph. Identifying clusters can be achieved by optimizing a fitness function that measures the quality of a cluster within the graph. Examples of such cluster measures include the conductance, the local and relative densities, and single cluster editing. We prove that the decision problems associated with the optimization tasks of finding clusters that are optimal with respect to these fitness measures are NP-complete.

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Author information

Authors and Affiliations

  1. Institute of Computer Science, Academy of Sciences of the Czech Republic, P. O. Box 5, 18207, Prague 8, Czech Republic

    Jiří Šíma

  2. Laboratory for Theoretical Computer Science, Helsinki University of Technology, TKK, P. O. Box 5400, FI-02015, Finland

    Satu Elisa Schaeffer

Authors
  1. Jiří Šíma
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  2. Satu Elisa Schaeffer
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Editor information

Editors and Affiliations

  1. Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou věží 2, 182 07, Prague 8, Czech Republic

    Jiří Wiedermann  & Július Štuller  & 

  2. Department of Information and Computer Sciences, University of Utrecht, P.O. Box 80.089, 3508, Utrecht, TB, The Netherlands

    Gerard Tel

  3. Faculty of Mathematics and Physics, Charles University, Prague

    Jaroslav Pokorný

  4. Institute of Informatics and Software Engineering Faculty of Informatics and Information technologies, Slovak University of Technology, Ilkovičova 3, 842 16, Bratislava

    Mária Bieliková

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© 2006 Springer-Verlag Berlin Heidelberg

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Šíma, J., Schaeffer, S.E. (2006). On the NP-Completeness of Some Graph Cluster Measures. In: Wiedermann, J., Tel, G., Pokorný, J., Bieliková, M., Štuller, J. (eds) SOFSEM 2006: Theory and Practice of Computer Science. SOFSEM 2006. Lecture Notes in Computer Science, vol 3831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11611257_51

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  • DOI: https://doi.org/10.1007/11611257_51

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31198-0

  • Online ISBN: 978-3-540-32217-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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