Advertisement

Communication-Efficient Construction of the Plane Localized Delaunay Graph

  • Prosenjit Bose
  • Paz Carmi
  • Michiel Smid
  • Daming Xu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6034)

Abstract

Let V be a finite set of points in the plane. We present a 2-local algorithm that constructs a plane \(\frac{4 \pi \sqrt{3}}{9}\)-spanner of the unit-disk graph \(\mathord{\it UDG}(V)\). Each node can only communicate with nodes that are within unit-distance from it. This algorithm only makes one round of communication and each point of V broadcasts at most 5 messages. This improves on all previously known message-bounds for this problem.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Araújo, F., Rodrigues, L.: Fast localized Delaunay triangulation. In: Higashino, T. (ed.) OPODIS 2004. LNCS, vol. 3544, pp. 81–93. Springer, Heidelberg (2005)Google Scholar
  2. 2.
    Bose, P., Carmi, P., Smid, M., Xu, D.: Communication-efficient construction of the plane localized Delaunay graph (2008), http://arxiv.org/abs/0809.2956
  3. 3.
    Bose, P., Maheshwari, A., Narasimhan, G., Smid, M., Zeh, N.: Approximating geometric bottleneck shortest paths. Computational Geometry: Theory and Applications 29, 233–249 (2004)zbMATHMathSciNetGoogle Scholar
  4. 4.
    Bose, P., Morin, P., Stojmenović, I., Urrutia, J.: Routing with guaranteed delivery in ad hoc wireless networks. Wireless Networks 7, 609–616 (2001)zbMATHCrossRefGoogle Scholar
  5. 5.
    Gao, J., Guibas, L.J., Hershberger, J., Zhang, L., Zhu, A.: Geometric spanners for routing in mobile networks. IEEE Journal on Selected Areas in Communications 23, 174–185 (2005)CrossRefGoogle Scholar
  6. 6.
    Karp, B., Kung, H.T.: GPSR: greedy perimeter stateless routing for wireless networks. In: Proceedings of the 6th Annual International Conference on Mobile Computing and Networking, pp. 243–254 (2000)Google Scholar
  7. 7.
    Keil, J.M., Gutwin, C.A.: Classes of graphs which approximate the complete Euclidean graph. Discrete & Computational Geometry 7, 13–28 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Li, X.-Y., Calinescu, G., Wan, P.-J., Wang, Y.: Localized Delaunay triangulation with applications in wireless ad hoc networks. IEEE Transactions on Parallel and Distributed Systems 14, 1035–1047 (2003)CrossRefGoogle Scholar
  9. 9.
    Narasimhan, G., Smid, M.: Geometric Spanner Networks. Cambridge University Press, Cambridge (2007)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Prosenjit Bose
    • 1
  • Paz Carmi
    • 2
  • Michiel Smid
    • 1
  • Daming Xu
    • 1
  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada
  2. 2.Department of Computer ScienceBen-Gurion UniversityBeer-ShevaIsrael

Personalised recommendations