Branch-and-price-and-cut on the clique partitioning problem with minimum clique size requirement

Given a complete graph K_n=(V,E)with edge weight c_e on each edge, we consider the problem of partitioning the vertices of graph K_n into subcliques that have at least S vertices, so as to minimize the total weight of the edges that have both endpoints in the same subclique. In this paper, we consider using the branch-and-price method to solve the problem. We demonstrate the necessity of cutting planes for this problem and suggest effective ways of adding cutting planes in the branch-and-price framework. The NP hard pricing problem is solved as an integer programming problem. We present computational results on large randomly generated problems.