A Branch-and-Cut to the Point-to-Point Connection Problem on Multicast Networks∗

In multicast routing, one of the basic problems consists of sending data from a set of sources to a set of destinations with minimum cost. A formalization of this problem using graph theory is given by the nonfixed Point-to-Point Connection (PPC) Problem. The optimization version of this problem is known to be NP-hard, and it can be also applied in areas such as circuit switching and VLSI design. We present a branch-and-cut approach to solve the PPC. Initially we describe a 0-1 integer programming formulation. Then, we prove that some of the constraints in this formulation are facet defining inequalities. Other valid inequalities, based on partitions of the set of vertices in the graph are also investigated. The proposed branch-and-cut algorithm is based on the previously discussed inequalities. Computational results of the branch-and-cut algorithm are presented, with comparisons to existing heuristic and approximation algorithms. The results show the effectiveness of the branch-and-cut method for instances of moderate size.