Isolation Concepts for Enumerating Dense Subgraphs

  • Christian Komusiewicz
  • Falk Hüffner
  • Hannes Moser
  • Rolf Niedermeier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4598)


In a graph G = (V,E), a vertex subset S ⊆ V of size k is called c-isolated if it has less than c·k outgoing edges. We repair a nontrivially flawed algorithm for enumerating all c-isolated cliques due to Ito et al. [European Symposium on Algorithms 2005] and obtain an algorithm running in O(4 c ·c 4·|E|) time. We describe a speedup trick that also helps parallelizing the enumeration. Moreover, we introduce a more restricted and a more general isolation concept and show that both lead to faster enumeration algorithms. Finally, we extend our considerations to s-plexes (a relaxation of the clique notion), pointing out a W[1]-hardness result and providing a fixed-parameter algorithm for enumerating isolated s-plexes.


Vertex Cover Outgoing Edge Minimal Vertex Enumeration Stage Isolation Condition 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Christian Komusiewicz
    • 1
  • Falk Hüffner
    • 1
  • Hannes Moser
    • 1
  • Rolf Niedermeier
    • 1
  1. 1.Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, D-07743 JenaGermany

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