Solving group Steiner problems as Steiner problems

Abstract

The generalized spanning tree or group Steiner problem (GSP) is a generalization of the Steiner problem in graphs (SPG): one requires a tree spanning (at least) one vertex of each subset, given in a family of vertex subsets, while minimizing the sum of the corresponding edge costs. Specialized solution procedures have been developed for this problem. In this paper we investigate the performance of a known but so far neglected transformation to the undirected Steiner problem in graphs. When combined with a recent metaheuristic for the SPG this straightforward approach compares favorably with specialized GSP heuristics. Thus we set a standard for future algorithms.