On sparse spanners of weighted graphs

Given a graphG, a subgraphG' is at-spanner ofG if, for everyu,v ɛV, the distance fromu tov inG' is at mostt times longer than the distance inG. In this paper we give a 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.