Genetic algorithms for the tree T-spanner problem

Abstract

The tree t-spanner problem is one of the most important spanning tree optimization problems and has different applications in communication networks and distributed systems. Let G = (V, E) be an undirected edge-weighted G = (V, E) with vertex set V and edge set E. We consider the problem of constructing a tree t-spanner T in G in the sense that the distance between every pair of vertices in T is at most t times the shortest distance between the two vertices in G. The value of t, called the stretch factor, quantifies the quality of the distance approximation of the corresponding tree t-spanner. The problem of finding a tree t-spanner with the smallest possible value of t is known as the Minimum Maximum Stretch Spanning Tree (MMST) problem. It is well known that, for any t ≥ 1, the problem of deciding whether G contains a tree t-spanner is NP-complete, thus, the MMST problem is NP-complete. In this paper, we present a genetic algorithm that returns a high quality solution for the MMST problem.