Parallel Greedy Algorithms for Steiner Forest

Abstract

The Steiner Forest Problem is a fundamental combinatorial optimization problem in operations research and computer science. Given an undirected graph with non-negative weights for edges and a set of pairs of vertices called terminals, the Steiner Forest Problem is to find the minimum cost subgraph that connects each of the terminal pairs together. We design a family of parallel greedy algorithms based on a sequential heuristic greedy algorithm called Paired Greedy, which iteratively connects the terminal pairs that have the minimum distance. The family of parallel algorithms consists of a set of algorithms exhibiting various degrees of parallelism determined by the number of pairs that are connected in parallel in each iteration of the algorithms. We implement and run the algorithms on a multi-core system and perform an extensive experimental analysis. We analyzed the performance of the algorithms on a rich library of Steiner Forest instances with various underlying graph types. The results show that our proposed parallel algorithms achieve significant speedup with respect to the sequential Paired Greedy algorithm and provide solutions with costs that are very close to those of the solutions obtained by the sequential Paired Greedy algorithm. We provide recommendation on selecting the type of parallel algorithm and its parameters in order to achieve the most efficient results for each class of instances.