Determining the Minimum Cost Steiner Tree for Delay Constrained Problems

Abstract

We address a variant of the Steiner tree problem for delay constrained problems. The addressed problem consists in determining the minimum cost Steiner tree, while guaranteeing that the delay between any two terminal nodes does not exceed a given maximum value. This problem is known as the bounded diameter Steiner minimum tree problem. We propose a compact formulation based on integer linear programming (ILP) to obtain optimal solutions, which was efficiently solved on two telecommunication core networks up to 75 nodes. However, given that for traditional Steiner tree graphs the ILP proved to be inefficient, we propose a heuristic method and compare it with the ILP formulation. We show that the heuristic provides optimal solutions, except for two cases in our experiments where it provided near-optimal solutions, always in reasonable runtimes. Additionally, to reduce the complexity of the problem, we propose some novel and modified graph reductions specific for the addressed problem.