Fixed-Parameter Algorithms for Cluster Vertex Deletion

Authors:
Falk Hüffner;Christian Komusiewicz;Hannes Moser;Rolf Niedermeier
Affiliations:
Friedrich-Schiller-Universität Jena, Institut für Informatik, Ernst-Abbe-Platz 2, 07743, Jena, Germany;Friedrich-Schiller-Universität Jena, Institut für Informatik, Ernst-Abbe-Platz 2, 07743, Jena, Germany;Friedrich-Schiller-Universität Jena, Institut für Informatik, Ernst-Abbe-Platz 2, 07743, Jena, Germany;Friedrich-Schiller-Universität Jena, Institut für Informatik, Ernst-Abbe-Platz 2, 07743, Jena, Germany
Venue:
Theory of Computing Systems - Special Section: Algorithmic Game Theory; Guest Editors: Burkhard Monien and Ulf-Peter Schroeder
Year:
2010

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Abstract

We initiate the first systematic study of the NP-hard Cluster Vertex Deletion (CVD) problem (unweighted and weighted) in terms of fixed-parameter algorithmics. In the unweighted case, one searches for a minimum number of vertex deletions to transform a graph into a collection of disjoint cliques. The parameter is the number of vertex deletions. We present efficient fixed-parameter algorithms for CVD applying the fairly new iterative compression technique. Moreover, we study the variant of CVD where the maximum number of cliques to be generated is prespecified. Here, we exploit connections to fixed-parameter algorithms for (weighted) Vertex Cover.