Connectivity of Graphs Induced by Directional Antennas

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◦, and establish upper and lower bounds for the minimum radius necessary to guarantee strong connectivity. In the case of 90◦ angles, we establish a lower bound of 2 and an upper bound of 7. In the case of 180 angles, we establish a lower bound of √ 3 and an upper bound of 1 + √ 3. Underlying our results is the assumption that the unit disk graph for S is connected.