Branch-and-cut approaches for p-Cluster Editing

This paper deals with a variant of the well-known Cluster Editing Problem (CEP), more precisely, the p-CEP, in which a given input graph should be edited by adding and/or removing edges in such a way that p vertex-disjoint cliques (clusters) are generated with the minimum number of editions. We introduce several valid inequalities where some of them turned out to be very effective when implemented in branch-and-cut approaches over two mathematical formulations. Computational experiments were carried out over a set of instances available in the CEP literature. The results obtained show the efficiency of the approaches according to the value of p, the graph density and the ratio between p and the number of vertices.