The edge-disjoing steiner problem in graphs

The Steiner Problem in Graphs is the problem of, given a weighted graph G and a subset S of the vertices of G, constructing a tree of minimum total weight connecting all the vertices in S. We consider an extension of this problem, called the Edge Disjolnt Steiner Problem In Graphs. It seeks to improve the reliability of the solution by requiring two (or more) seperate trees spanning S. Finding a feasible solution to this problem is shown to be NP-complete. Two relaxations of the problem are presented, which are used to compute a lower bound to the problem. Both relaxations can also be exploited for upper bound generation. Computational results are given for graphs with up to 100 vertices and 4950 edges.