Advertisement

Strong Connectivity of Sensor Networks with Double Antennae

  • Mohsen Eftekhari Hesari
  • Evangelos Kranakis
  • Fraser MacQuarie
  • Oscar Morales-Ponce
  • Lata Narayanan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7355)

Abstract

Inspired by the well-known Dipole and Yagi antennae we introduce and study a new theoretical model of directional antennae that we call double antennae. Given a set P of n sensors in the plane equipped with double antennae of angle φ and with dipole-like and Yagi-like antenna propagation patterns, we study the connectivity and stretch factor problems, namely finding the minimum range such that double antennae of that range can be oriented so as to guarantee strong connectivity or stretch factor of the resulting network. We introduce the new concepts of (2,φ)-connectivity and φ-angular range r φ (P) and use it to characterize the optimality of our algorithms. We prove that r φ (P) is a lower bound on the range required for strong connectivity and show how to compute r φ (P) in time polynomial in n. We give algorithms for orienting the antennae so as to attain strong connectivity using optimal range when φ ≥ 2 π/3, and algorithms approximating the range for φ ≥ π/2. For φ < π/3, we show that the problem is NP-complete to approximate within a factor \(\sqrt{3}\). For φ ≥ π/2, we give an algorithm to orient the antennae so that the resulting network has a stretch factor of at most 4 compared to the underlying unit disk graph.

Keywords

Connectivity Double Antenna Range Stretch Factor Unit Disk Graph 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    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
  2. 2.
    Caragiannis, I., Kaklamanis, C., Kranakis, E., Krizanc, D., Wiese, A.: Communication in wireless networks with directional antennas. In: Proceedings of the Twentieth Annual Symposium on Parallelism in Algorithms and Architectures, pp. 344–351. ACM (2008)Google Scholar
  3. 3.
    Cormen, T.H.: Introduction to Algorithms, 2nd edn. The MIT Press (2007)Google Scholar
  4. 4.
    Damian, M., Flatland, R.: Spanning properties of graphs induced by directional antennas. In: Electronic Proc. 20th Fall Workshop on Computational Geometry. Stony Brook University, Stony Brook (2010)Google Scholar
  5. 5.
    De Berg, M., Cheong, O., Van Kreveld, M.: Computational geometry: algorithms and applications. Springer-Verlag New York Inc. (2008)Google Scholar
  6. 6.
    Dobrev, S., Kranakis, E., Krizanc, D., Opatrny, J., Ponce, O.M., Stacho, L.: Strong Connectivity in Sensor Networks with Given Number of Directional Antennae of Bounded Angle. In: Wu, W., Daescu, O. (eds.) COCOA 2010, Part II. LNCS, vol. 6509, pp. 72–86. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  7. 7.
    Fleischner, H.: The square of every two-connected graph is hamiltonian. Journal of Combinatorial Theory, Series B 16(1), 29–34 (1974)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Gupta, H., Kumar, U., Das, S.R.: A topology control approach to using directional antennas in wireless mesh networks. IEEE International Conference on Communications 9(06), 4083–4088 (2006)Google Scholar
  9. 9.
    Gupta, P., Kumar, P.R.: The capacity of wireless networks. IEEE Transactions on Information Theory 46(2), 388–404 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Hu, L., Evans, D.: Using directional antennas to prevent wormhole attacks. In: Network and Distributed System Security Symposium, NDSS (2004)Google Scholar
  11. 11.
    Kranakis, E., Krizanc, D., Morales, O.: Maintaining connectivity in sensor networks using directional antennae. In: Nikoletseas, S., Rolim, J. (eds.) Theoretical Aspects of Distributed Computing in Sensor Networks, pp. 59–84 (2010)Google Scholar
  12. 12.
    Kranakis, E., Krizanc, D., Williams, E.: Directional Versus Omnidirectional Antennas for Energy Consumption and k-Connectivity of Networks of Sensors. In: Higashino, T. (ed.) OPODIS 2004. LNCS, vol. 3544, pp. 357–368. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  13. 13.
    Parker, R.G., Rardin, R.L.: Guaranteed performance heuristics for the bottleneck travelling salesman problem. Operations Research Letters 2(6), 269–272 (1984)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Schiller, J.H.: Mobile Communications. Addison Wesley (2003)Google Scholar
  15. 15.
    Yi, S., Pei, Y., Kalyanaraman, S., Azimi-Sadjadi, B.: How is the capacity of ad hoc networks improved with directional antennas? Wireless Networks 13(5), 635–648 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Mohsen Eftekhari Hesari
    • 1
  • Evangelos Kranakis
    • 2
  • Fraser MacQuarie
    • 2
  • Oscar Morales-Ponce
    • 2
  • Lata Narayanan
    • 1
  1. 1.Department of Computer Science and Software EngineeringConcordia UniversityMontrealCanada
  2. 2.School of Computer ScienceCarleton UniversityOttawaCanada

Personalised recommendations