A New Branch and Bound Algorithm for the Clique Partitioning Problem

This paper considers the problem of clustering the vertices of a complete, edge weighted graph. The objective is to maximize the edge weights within the clusters (also called cliques). This so called Clique Partitioning Problem (CPP) is NP-complete, but it has several real life applications such as groupings in exible manufacturing systems, in biology, in flight gate assignment, etc.. Numerous heuristic and exact approaches as well as benchmark tests have been presented in the literature. Most exact methods use branch and bound with branching over edges. We present tighter upper bounds for each search tree node than those known from literature, improve constraint propagation techniques for fixing edges in each node, and present a new branching scheme