A More Effective Linear Kernelization for Cluster Editing

In the NP-hard Cluster Editing problem, we have as input an undirected graph G and an integer k 0. The question is whether we can transform G, by inserting and deleting at most k edges, into a cluster graph, that is, a union of disjoint cliques. We first confirm a conjecture by Michael Fellows [IWPEC 2006] that there is a polynomialtime kernelization for Cluster Editing that leads to a problem kernel with at most 6k vertices. More precisely, we present a cubic-time algorithm that, given a graph G and an integer k 0, finds a graph G and an integer k k such that G can be transformed into a cluster graph by at most k edge modifications iff G can be transformed into a cluster graph by at most k edge modifications, and the problem kernel G has at most 6k vertices. So far, only a problem kernel of 24k vertices was known. Second, we show that this bound for the number of vertices of G can be further improved to 4k. Finally, we consider the variant of Cluster Editing where the number of cli...

• Type: Conference
• Year: 2007
• Where: ESCAPE
• Authors: Jiong Guo
• Keywords: Algorithms, Cluster Editing, Cluster Graph, ESCAPE 2007, Problem Kernel