Approximation Algorithms for Minimum Energy Bounded-Hop Strong Connectivity Range Assignment in Ad-hoc Networks

This paper concerns the range assignment problem in static ad-hoc networks on metric spaces. We focus on the bounded-hop strong-connectivity problem (hSC) on general metric spaces for constant h. Given a nite set of locations S on a metric space and a positive integer 1 h < jSj, the Min-Range(hSC) problem requires assigning a transmission range to each station so as to minimize the total power con-sumption, while facilitating communication between any two stations with at most h hops. When h 2isapositive constant and when the locations of S are represented as points in a general metric space, we provide a polynomial-time algorithm yielding a constant approximation for Min-Range(hSC). In addition, for nonconstant h we show that there exists a probabilistic O(n log n log log n)-approximation algorithm on general metric spaces for the Min-Range(hSC) problem