Abstract
We introduce the NP-hard graph-based data clustering problem s -Plex Cluster Vertex Deletion, where the task is to delete at most k vertices from a graph so that the connected components of the resulting graph are s-plexes. In an s-plex, every vertex has an edge to all but at most s − 1 other vertices; cliques are 1-plexes. We propose a new method for kernelizing a large class of vertex deletion problems and illustrate it by developing an O(k 2 s 3)-vertex problem kernel for s -Plex Cluster Vertex Deletion that can be computed in O(ksn 2) time, where n is the number of graph vertices. The corresponding “kernelization through tidying” exploits polynomial-time approximation results.
Supported by the DFG, project AREG, NI 369/9.
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van Bevern, R., Moser, H., Niedermeier, R. (2010). Kernelization through Tidying. In: López-Ortiz, A. (eds) LATIN 2010: Theoretical Informatics. LATIN 2010. Lecture Notes in Computer Science, vol 6034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12200-2_46
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DOI: https://doi.org/10.1007/978-3-642-12200-2_46
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