TY - GEN

T1 - Do directional antennas facilitate in reducing interferences?

AU - Aschner, Rom

AU - Katz, Matthew J.

AU - Morgenstern, Gila

N1 - Funding Information:
Work by R. Aschner was partially supported by the Lynn and William Frankel Center for Computer Sciences and by the Israel Ministry of Industry, Trade and Labor (consortium CORNET). Work by M.J. Katz was partially supported by the Israel Ministry of Industry, Trade and Labor (consortium CORNET), by grant 1045/10 from the Israel Science Foundation, and by grant 2010074 from the United States – Israel Binational Science Foundation. Work by G. Morgenstern was partially supported by the Lynn and William Frankel Center for Computer Sciences and by the Caesarea Rothschild Institute (CRI).

PY - 2012/7/4

Y1 - 2012/7/4

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=84863100988&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-31155-0_18

DO - 10.1007/978-3-642-31155-0_18

M3 - Conference contribution

AN - SCOPUS:84863100988

SN - 9783642311543

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 201

EP - 212

BT - Algorithm Theory, SWAT 2012 - 13th Scandinavian Symposium and Workshops, Proceedings

T2 - 13th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2012

Y2 - 4 July 2012 through 6 July 2012

ER -