κ-clustering minimum biclique completion via a hybrid CP and SDP approach

Abstract

This paper presents a hybrid Constraint Programming (CP) and Semidefinite Programming (SDP) approach to the k-clustering minimum biclique completion problem on bipartite graphs. The problem consists in partitioning a bipartite undirected graph into k clusters such that the sum of the edges that complete each cluster into a biclique, i.e., a complete bipartite subgraph, is minimum. The problem arises in telecommunications, in particular in bundling channels in multicast transmissions. In literature, the problem has been tackled with an Integer Bilinear Programming approach. We introduce two quasi-biclique constraints and we propose a SDP relaxation of the problem that provides much stronger lower bounds than the Bilinear Programming relaxation. The quasi-biclique constraints and the SDP relaxation are integrated into a hybrid CP and SDP approach. Computational results on a set of random instances provide further evidence about the potential of CP and SDP hybridizations. © 2009 Springer Berlin Heidelberg.