Parallelization of local search for Euclidean Steiner tree problem

Abstract

The Euclidean Steiner tree problem is to find the tree with minimal Euclidean length spanning a given fixed points in the plane, allowing the addition of auxiliary points known as Steiner points. Parallel implementations of local search algorithm are an effective technique to speed up the search for a solution of Steiner tree problem. This technique not only allows to solve larger Steiner tree problem or to find improved solutions with respect to their sequential counterparts, but also it leads to further robustness in the algorithm. In this paper, we concentrate on the problem of finding a Euclidean Steiner tree using parallel local search technique. The main contribution of this work is the O(n2 log2 n+log n log(n/log n)) parallel local search algorithm for computing Steiner tree on the Euclidean plane. The main advantage of the algorithm is that it does not need synchronization. As a result, it has no communication overhead.