Clustering with partial information

The Correlation Clustering problem, also known as the Cluster Editing problem, seeks to edit a given graph by adding and deleting edges to obtain a collection of disconnected cliques, such that the editing cost is minimized. The Edge Clique Partition problem seeks to partition the edges of a given graph into edge disjoint cliques, such that the number of cliques is minimized. Both problems are naturally NP-hard, and they are well studied with respect to approximation and fixed parameter tractability. In this paper we study these two problems in a more general setting, where the input graphs miss some information, meaning that whether or not there is an edge between some pairs of vertices is not decided in advance. On such graphs the problems are previously studied only for approximation. For both problems, we give parameterized algorithms through kernelization. For the first problem, we show fixed parameter tractability when the parameters are the editing cost and the minimum numbe...

• Type: Journal
• Year: 2010
• Where: TCS
• Authors: Hans L. Bodlaender, Michael R. Fellows, Pinar Heggernes, Federico Mancini, Charis Papadopoulos, Frances A. Rosamond
• Keywords: Cliques, Parameters, TCS 2010, Theoretical Computer Science, Undecided Edges