LDS vs FPT Method for Cluster Deletion

We consider the following vertex-partition problem on graphs: given a simple graph G = (V, E), we want to partition G into a disjoint union of cliques by only removing a minimum number of edges. This NP-hard optimization problem is referred to as the Cluster Deletion (CD). In this paper, we propose an encoding of CD in terms of a Weighted Constraint Satisfaction Problem (WCSP), a framework which has been widely used in solving hard combinatorial problems. We compare our approach with a fixed-parameter tractability algorithm, one of the most used algorithms for solving cluster deletion. Then, we experimentally show that significant results are obtained using the WCSP encoding. We compare both solution quality and running times of these algorithms on random graphs and protein similarity graphs derived from the COG dataset.