Generalized Graph Clustering: Recognizing (p,q)-Cluster Graphs

  • Pinar Heggernes
  • Daniel Lokshtanov
  • Jesper Nederlof
  • Christophe Paul
  • Jan Arne Telle
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6410)


Cluster Editing is a classical graph theoretic approach to tackle the problem of data set clustering: it consists of modifying a similarity graph into a disjoint union of cliques, i.e, clusters. As pointed out in a number of recent papers, the cluster editing model is too rigid to capture common features of real data sets. Several generalizations have thereby been proposed. In this paper, we introduce (p,q)-cluster graphs, where each cluster misses at most p edges to be a clique, and there are at most q edges between a cluster and other clusters. Our generalization is the first one that allows a large number of false positives and negatives in total, while bounding the number of these locally for each cluster by p and q. We show that recognizing (p,q)-cluster graphs is NP-complete when p and q are input. On the positive side, we show that (0,q)-cluster, (p,1)-cluster, (p,2)-cluster, and (1,3)-cluster graphs can be recognized in polynomial time.


Polynomial Time Disjoint Union Input Graph Reduction Rule Cluster Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Pinar Heggernes
    • 1
  • Daniel Lokshtanov
    • 1
  • Jesper Nederlof
    • 1
  • Christophe Paul
    • 2
  • Jan Arne Telle
    • 1
  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.CNRS, LIRMMUniversité Montpellier 2France

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