Switching to Directional Antennas with Constant Increase in Radius and Hop Distance

摘要

For any angle a < 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 a and radius r_(dir), for some constant r_(dir) = r_(dir)(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.