A Branch-and-price Approach to the k-Clustering Minimum Biclique Completion Problem

Given a bipartite graph G = (S, T, E), we consider the problem of finding k bipartite subgraphs, called "clusters", such that each vertex i of S appears in exactly one of them, every vertex j of T appears in each cluster in which at least one of its neighbors appears, and the total number of edges needed to make each cluster complete (i.e. to become a biclique) is minimised. This problem is known as k-clustering Minimum Biclique Completion Problem (kMinBCP) and has been shown strongly NP-hard. It has applications in bundling channels for multicast transmissions. We present several Integer Programming formulations, and a SDP relaxation, to motivate the choice of a Branch-andPrice algorithm with a non-trivial branching rule, which takes advantage of a new metaheuristic based on Variable Neighborhood Unfeasible Search (VNUS). Extensive computational results show that this approach outperforms other state-of-the-art approaches proposed in the literature, allowing to solve to opt...

• Type: Journal
• Year: 2010
• Where: COLOGNETWENTE
• Authors: Stefano Gualandi, Francesco Maffioli, Claudio Magni
• Keywords: Biclique Completion Problem, COLOGNETWENTE 2010, Neighborhood Unfeasible Search, Optimization, Variable Neighborhood