A branch-and-price algorithm for the Steiner tree packing problem

This paper deals with the Steiner tree packing problem. For a given undirected graph G=(V,E) with positive integer capacities and non-negative weights on its edges, and a list of node sets (nets), the problem is to find a connection of nets which satisfies the edge capacity limits and minimizes the total weights. We focus on the switchbox routing problem in knock-knee model and formulate this problem as an integer programming using Steiner tree variables. We develop a branch-and-price algorithm. The algorithm is applied on some standard test instances and we compare the performances with the results using cutting-plane approach. Computational results show that our algorithm is competitive to the cutting plane algorithm presented by Grötschel et al. and can be used to solve practically sized problems.