A parallel algorithm for the Steiner tree problem

The Steiner problem in graphs is to find the minimum cost tree which spans at least a given subset of V, where V is the set of vertices in the graph. This problem has a wide variety of practical applications, including wire routing in physical VLSI design. Since the problem is NP-complete, much work has been devoted to developing approximate solutions such as the one proposed by V.J. Rayward-Smith (1988). In this paper, we identify the Rayward-Smith´s algorithm as being appropriate for parallelization, and describe a parallel implementation of that algorithm. We also show that linear speedup is achievable on the PRAM model with the number of processors p⩽|V|