Advertisement

Do Directional Antennas Facilitate in Reducing Interferences?

  • Rom Aschner
  • Matthew J. Katz
  • Gila Morgenstern
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).

Keywords

Connected Graph Maximum Range Symmetric Model Directional Antenna Topology Control 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ackerman, E., Gelander, T., Pinchasi, R.: Ice-creams and wedge graphs. CoRR abs/1106.0855 (2011)Google Scholar
  2. 2.
    Aschner, R., Katz, M.J., Morgenstern, G.: Symmetric connectivity with directional antennas. CoRR abs/1108.0492 (2011)Google Scholar
  3. 3.
    Bose, P., Carmi, P., Damian, M., Flatland, R., Katz, M.J., Maheshwari, A.: Switching to Directional Antennas with Constant Increase in Radius and Hop Distance. In: Dehne, F., Iacono, J., Sack, J.-R. (eds.) WADS 2011. LNCS, vol. 6844, pp. 134–146. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  4. 4.
    Burkhart, M., von Rickenbach, P., Wattenhofer, R., Zollinger, A.: Does topology control reduce interference? In: Proc. 5th ACM Internat. Sympos. on Mobile Ad Hoc Networking and Computing, pp. 9–19 (2004)Google Scholar
  5. 5.
    Caragiannis, I., Kaklamanis, C., Kranakis, E., Krizanc, D., Wiese, A.: Communication in wireless networks with directional antennas. In: 20th ACM Sympos. on Parallelism in Algorithms and Architectures, pp. 344–351 (2008)Google Scholar
  6. 6.
    Carmi, P., Katz, M.J., Lotker, Z., Rosén, A.: Connectivity guarantees for wireless networks with directional antennas. Computational Geometry: Theory and Applications 44(9), 477–485 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Carmi, P., Katz, M.J., Mitchell, J.S.B.: The minimum-area spanning tree problem. Computational Geometry: Theory and Applications 35(3), 218–225 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Damian, M., Flatland, R.: Spanning properties of graphs induced by directional antennas. In: Electronic Proc. 20th Fall Workshop on Computational Geometry. Stony Brook, NY (2010)Google Scholar
  9. 9.
    Erdös, P., Szekeres, G.: A combinatorial problem in geometry. Compositio Mathematica 2, 463–470 (1935)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Halldórsson, M.M., Tokuyama, T.: Minimizing interference of a wireless ad-hoc network in a plane. Theor. Comput. Sci. 402(1), 29–42 (2008)zbMATHCrossRefGoogle Scholar
  11. 11.
    Johansson, T., Carr-Motycková, L.: Reducing interference in ad hoc networks through topology control. In: Proc. of the 2005 Joint Workshop on Foundations of Mobile Computing, pp. 17–23 (2005)Google Scholar
  12. 12.
    Korman, M.: Minimizing Interference in Ad-Hoc Networks with Bounded Communication Radius. In: Asano, T., Nakano, S.-i., Okamoto, Y., Watanabe, O. (eds.) ISAAC 2011. LNCS, vol. 7074, pp. 80–89. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  13. 13.
    Kranakis, E., Krizanc, D., Morales, O.: Maintaining connectivity in sensor networks using directional antennae. In: Nikoletseas, S., Rolim, J.D.P. (eds.) Theoretical Aspects of Distributed Computing in Sensor Networks, ch. 3, pp. 59–84. Springer (2011)Google Scholar
  14. 14.
    Moaveni-Nejad, K., Li, X.-Y.: Low-interference topology control for wireless ad hoc networks. Ad Hoc & Sensor Wireless Networks 1(1-2) (2005)Google Scholar
  15. 15.
    von Rickenbach, P., Schmid, S., Wattenhofer, R., Zollinger, A.: A robust interference model for wireless ad-hoc networks. In: Proc. 19th IEEE Internat. Parallel and Distributed Processing Sympos. (2005)Google Scholar
  16. 16.
    Tan, H., Lou, T., Lau, F.C.M., Wang, Y., Chen, S.: Minimizing Interference for the Highway Model in Wireless Ad-Hoc and Sensor Networks. In: Černá, I., Gyimóthy, T., Hromkovič, J., Jefferey, K., Králović, R., Vukolić, M., Wolf, S. (eds.) SOFSEM 2011. LNCS, vol. 6543, pp. 520–532. Springer, Heidelberg (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Rom Aschner
    • 1
  • Matthew J. Katz
    • 1
  • Gila Morgenstern
    • 2
  1. 1.Department of Computer ScienceBen-Gurion UniversityIsrael
  2. 2.Caesarea Rothschild InstituteUniversity of HaifaIsrael

Personalised recommendations