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ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Exact algorithms for cluster editing: evaluation and experiments
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
Improved algorithms for bicluster editing
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Fixed-parameter algorithms for cluster vertex deletion
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Polynomial kernels for 3-leaf power graph modification problems
Discrete Applied Mathematics
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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 cliques that the cluster graph can contain is stipulated to be a constant d 0. We present a simple kernelization for this variant leaving a problem kernel of at most (d+2)k +d vertices.