A Heuristic For The Bounded Diameter Minimum Spanning Tree Problem

Given a connected, edge-weighted and undirected complete graph G(V,E,w), the bounded diameter minimum spanning tree (BD-MST) problem deals with finding a spanning tree T of minimum cost in such a way that the diameter of T should not exceed D >= 2, where D is a given positive integer. This problem is NP-hard for 4 <= D < vertical bar V vertical bar - 1. In this paper, we present a problem-specific heuristic (Heu_BDMST) for the BD-MST problem. Heu_BDMST is a greedy approach that combines the concept of the Kruskal algorithm and the shortest path algorithm. On a set of benchmark Euclidean and non-Euclidean instances, Heu_BDMST is effective in comparison to well-known problem-specific heuristics in the literature.