Construction of Minimum-Weight Spanners

Spanners are sparse subgraphs that preserve distances up to a given factor in the underlying graph. Recently spanners have found important practical applications in metric space searching and message distribution in networks. These applications use some variant of the socalled greedy algorithm for constructing the spanner — an algorithm that mimics Kruskal’s minimum spanning tree algorithm. Greedy spanners have nice theoretical properties, but their practical performance with respect to total weight is unknown. In this paper we give an exact algorithm for constructing minimum-weight spanners in arbitrary graphs. By using the solutions (and lower bounds) from this algorithm, we experimentally evaluate the performance of the greedy algorithm for a set of realistic problem instances.