Generating sparse spanners for weighted graphs

Abstract

Given a graph G, a subgraph G’ is a it-spanner of G, if for every u, v ∊ V, the distance from u to v in G’ is at most t times longer than the distance in G. In this paper we give a very simple algorithm for constructing sparse spanners for arbitrary weighted graphs. We then apply this algorithm to obtain specific results for planar graphs and Euclidean graphs. We discuss the optimality of our results and present several nearly matching lower bounds.