Given the positions of n sites in a radio network we consider the problem of finding routes between any pair of sites that minimize energy consumption and do not use more than some constant number k of hops. Known exact algorithms for this problem required Ω(n logn) per query pair (p, q). In this paper we relax the exactness requirement and only compute approximate (1+2) solutions which allows ...

Given a real number t > 1, a geometric t-spanner is a geometric graph for a point set in R with straight lines between vertices such that the ratio of the shortest-path distance between every pair of vertices in the graph (with Euclidean edge lengths) to their actual Euclidean distance is at most t. An imprecise point set is modeled by a set R of regions in R. If one chooses a point in each reg...