Parallel Minimum Spanning Tree Heuristic for the Steiner Problem in Graphs

Given an undirected graph with weights associated with its edges, the Steiner tree problem consists of finding a minimum weight subtree spanning a given subset of (terminal) nodes of the original graph. Minimum Spanning Tree Heuristic (MSTH) is a heuristic for solving the Steiner problem in graphs. In this paper we first review existing algorithms for solving the Steiner problem in graphs. We then introduce a new parallel version of MSTH on three dimensional mesh of trees architecture. We describe our algorithm and analyze its time complexity. The time complexity analysis shows that the algorithm's running time is (lg) 2 O n which is comparable with other existing parallel solutions. 1