Strong connectivity in sensor networks with given number of directional antennae of bounded angle

Abstract

Given a set S of n sensors in the plane we consider the problem of establishing an ad hoc network from these sensors using directional antennae. We prove that for each given integer 1 ≤ k ≤ 5 there is a strongly connected spanner on the set of points so that each sensor uses at most k such directional antennae whose range differs from the optimal range by a multiplicative factor of at most 2·sin (π/k+1). Moreover, given a minimum spanning tree on the set of points the spanner can be constructed in additional O(n) time. In addition, we prove NP completeness results for k = 2 antennae. © 2010 Springer-Verlag.