Do directional antennas facilitate in reducing interferences?

• Authors: Rom Aschner;Matthew J. Katz;Gila Morgenstern
• Venue: SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
• Year: 2012

The coverage area of a directional antenna located at point p is a circular sector of angle α, whose orientation and radius can be adjusted. The interference at p, denoted I(p), is the number of antennas that cover p, and the interference of a communication graph G=(P,E) is I(G)= max {I(p) : p∈P}. In this paper we address the question in its title. That is, we study several variants of the following problem: What is the minimum interference I, such that for any set P of n points in the plane, representing transceivers equipped with a directional antenna of angle α, one can assign orientations and ranges to the points in P, so that the induced communication graph G is either connected or strongly connected and I(G)≤I. In the asymmetric model (i.e., G is required to be strongly connected), we prove that I=O(1) for απ/3, in contrast with I=Θ(logn) for α=2π, proved by Korman [12]. In the symmetric model (i.e., G is required to be connected), the situation is less clear. We show that I=Θ(n) for απ/2, and prove that $I=O(\sqrt{n})$ for π/2≤α≤3π/2, by applying the Erdös-Szekeres theorem. The corresponding result for α=2π is $I=\Theta(\sqrt{n})$, proved by Halldórsson and Tokuyama [10]. As in [12] and [10] who deal with the case α=2π, in both models, we assign ranges that are bounded by some constant c, assuming that UDG(P) (i.e., the unit disk graph over P) is connected. Moreover, the $O(\sqrt{n})$ bound in the symmetric model reduces to $O(\sqrt{\Delta})$, where Δ is the maximum degree in UDG(P).