Switching to directional antennas with constant increase in radius and hop distance

Abstract

For any angle α < 2π, we show that any connected communication graph that is induced by a set P of n transceivers using omni-directional antennas of radius 1, can be replaced by a strongly connected communication graph, in which each transceiver in P is equipped with a directional antenna of angle α and radius rdir, for some constant rdir = rdir(α). Moreover, the new communication graph is a c-spanner of the original graph, for some constant c = c(α), with respect to number of hops. © 2011 Springer-Verlag.