# Do directional antennas facilitate in reducing interferences?

Rom Aschner, Matthew J. Katz, Gila Morgenstern

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

16 Scopus citations

## 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 for π/2 ≤ α ≤ 3π/2, by applying the Erdös-Szekeres theorem. The corresponding result for α = 2π is , 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 bound in the symmetric model reduces to , where Δ is the maximum degree in UDG(P).

Original language English Algorithm Theory, SWAT 2012 - 13th Scandinavian Symposium and Workshops, Proceedings 201-212 12 https://doi.org/10.1007/978-3-642-31155-0_18 Published - 4 Jul 2012 13th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2012 - Helsinki, FinlandDuration: 4 Jul 2012 → 6 Jul 2012

### Publication series

Name Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 7357 LNCS 0302-9743 1611-3349

### Conference

Conference 13th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2012 Finland Helsinki 4/07/12 → 6/07/12

## ASJC Scopus subject areas

• Theoretical Computer Science
• General Computer Science

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