Kernelization through Tidying

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(k2 s3 )-vertex problem kernel for s-Plex Cluster Vertex Deletion that can be computed in O(ksn2 ) time, where n is the number of graph vertices. The corresponding “kernelization through tidying” exploits polynomial-time approximation results.

• Type: Conference
• Year: 2010
• Where: LATIN
• Authors: René van Bevern, Hannes Moser, Rolf Niedermeier
• Keywords: Cluster Vertex Deletion, Information Retrieval, LATIN 2010, S-plex Cluster Vertex, Vertex Deletion Problems