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 O(lg² n) which is comparable with other existing parallel solutions.