Biclique completion problems for multicast network design

This paper considers the problem of aggregating several multicast sessions. A multicast session is defined as a subset of clients requiring the same information. Besides, each client can require several multicast sessions. A telecommunication network cannot manage many multicast sessions at the same time. It is hence necessary to group the sessions into a limited number of clusters. The problem then consists in aggregating the sessions into clusters to limit the number of unnecessary information sent to clients. The strong relationship of the problems with biclique problems in bipartite graph is established. We then model the problems using integer quadratic and linear programming formulations. We investigate some properties to strengthen the models. Several algorithms are provided and compared with a series of numerical experiments.