A Parallel Approximation Algorithm for the Steiner Forest Problem

In the Steiner Forest problem, we are given an undirected graph with non-negative weights for edges, a set of pairs of vertices, called terminals, and the goal is to find the minimum cost subgraph that connects each of the terminal pairs together. There exist several sequential heuristic and approximation algorithms for the Steiner Forest problem. In practice, the primal-dual 2-approximation algorithm is one of the fastest and obtains solutions that are very close to the optimal solution. In this paper, we design a practical parallel approximation algorithm based on the primal-dual sequential algorithm. The parallel algorithm maintains the approximation guarantees of the sequential primal-dual algorithm and it is specifically designed for execution on multi-core computers. We implement and run the parallel algorithm on a multi-core system with a large number of cores and perform an extensive experimental performance analysis on randomly generated graphs. The results show that our proposed parallel approximation algorithm achieves a significant speedup with respect to the sequential primal-dual algorithm.