On the NP-Completeness of some graph cluster measures

  • Authors:
  • Jiří Šíma;Satu Elisa Schaeffer

  • Affiliations:
  • Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 8, Czech Republic;Laboratory for Theoretical Computer Science, Helsinki University of Technology, TKK, Finland

  • Venue:
  • SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
  • Year:
  • 2006

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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.