Generating sparse 2-spanners

A k-spanner of a connected graph G = (V, E) is a subgraph G′ consisting of all the vertices of V and a subset of the edges, with the additional property that the distance between any two vertices in G′ is larger than that distance in G by no more than a factor of k. This note concerns the problem of finding the sparsest 2-spanner in a given graph and presents an approximation algorithm for this problem with approximation ratio log(|E|/|V|).