SWAT 2012: Algorithm Theory – SWAT 2012 pp 201-212

# Do Directional Antennas Facilitate in Reducing Interferences?

• Rom Aschner
• Matthew J. Katz
• Gila Morgenstern
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7357)

## Abstract

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 α < 2π/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 α < π/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).

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