An SST-based algorithm for the steiner problem in graphs

In this paper we consider the Steiner problem in graphs which is the problem of connecting together, at minimum cost, a number of vertices in an undirected graphs. We present a formulation of the problem as a shortest spanning tree (SST) problem with additional constraints. By relaxing thses additional constraints in a lagrangean fashion we obtain a lower bound for the problem based upon the solution of an unconstrained SST problem. Problem reduction tests derived from both the original problem and the lagrangean relaxation are given. Incorporating the bound and the reduction tests into a tree search procedure enables us to solve problems involving the connection of up to 1250 vertices in a graph with 62500 edges and 2500 vertices.

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