Connectivity of Graphs Induced by Directional Antennas

Abstract

This paper addresses the problem of finding an orientation and a minimum radius for directional antennas of a fixed angle placed at the points of a planar set S, that induce a strongly connected communication graph. We consider problem instances in which antenna angles are fixed at 90 and 180 degrees, and establish upper and lower bounds for the minimum radius necessary to guarantee strong connectivity. In the case of 90-degree angles, we establish a lower bound of 2 and an upper bound of 7. In the case of 180-degree angles, we establish a lower bound of sqrt(3) and an upper bound of 1+sqrt(3). Underlying our results is the assumption that the unit disk graph for S is connected.