Graph-based data clustering with overlaps

  • Authors:

  • Michael R. Fellows;Jiong Guo;Christian Komusiewicz;Rolf Niedermeier;Johannes Uhlmann

  • Affiliations:

  • PC Research Unit, Office of DVC (Research), Charles Darwin University, Darwin, Northern Territory 0909, Australia;Universität des Saarlandes, Campus E 1.4, D-66123 Saarbrücken, Germany;Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz2, D-07743 Jena, Germany;Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz2, D-07743 Jena, Germany;Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz2, D-07743 Jena, Germany

  • Venue:
  • Discrete Optimization
  • Year:
  • 2011

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Abstract

We introduce overlap cluster graph modification problems where, other than in most previous works, the clusters of the target graph may overlap. More precisely, the studied graph problems ask for a minimum number of edge modifications such that the resulting graph consists of clusters (that is, maximal cliques) that may overlap up to a certain amount specified by the overlap number s. In the case of s-vertex-overlap, each vertex may be part of at most s maximal cliques; s-edge-overlap is analogously defined in terms of edges. We provide a complexity dichotomy (polynomial-time solvable versus NP-hard) for the underlying edge modification problems, develop forbidden subgraph characterizations of ''cluster graphs with overlaps'', and study the parameterized complexity in terms of the number of allowed edge modifications, achieving fixed-parameter tractability (in case of constant s-values) and parameterized hardness (in case of unbounded s-values).