Routing Properties of the Localized Delaunay Triangulation over Heterogeneous Ad-Hoc Wireless Networks

  • Mark D. Watson
  • J. Mark Keil
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3980)


We explore the extremal properties of the Localized Delaunay Triangulation over networks with heterogeneous ranges. We find theoretical bounds on these properties and compare them with those found via experimentation.


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  1. 1.
    Kuhn, F., Wattenhofer, R., Zhang, Y., Zollinger, A.: Geometric ad-hoc routing: Of theory and practice. In: Proc. 22nd ACM Int. Symposium on the Principles of Distributed Computing, PODC (2003)Google Scholar
  2. 2.
    Li, X.Y., Calinescu, G., Wan, P.J.: Distributed construction of planar spanner and routing for ad hoc wireless networks. In: Proceedings IEEE INFOCOM 2002, The 21st Annual Joint Conference of the IEEE Computer and Communications Societies, New York, USA, June 23-27. IEEE, Los Alamitos (2002)Google Scholar
  3. 3.
    Li, X.Y., Song, W.Z., Wang, Y.: Efficient topology control for wireless ad hoc networks with non-uniform transmission ranges. ACM Wireless Networks 11(3) (2005)Google Scholar
  4. 4.
    Li, X.Y.: Applications of computational geometry in wireless ad hoc networks. In: Cheng, X., Huang, X., Du, D.Z. (eds.) Ad Hoc Wireless Networking, pp. 1–68. Kluwer, Dordrecht (2003)Google Scholar
  5. 5.
    Kapoor, S., Li, X.Y.: Proximity structures for geometric graphs. In: Dehne, F., Sack, J.-R., Smid, M. (eds.) WADS 2003. LNCS, vol. 2748, pp. 365–376. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  6. 6.
    Chew, P.: There is a planar graph as good as the complete graph. In: Proceedings of the 2nd Symposium on Computation Geometry, pp. 564–567 (1986)Google Scholar
  7. 7.
    Peleg, D., Schaffer, A.A.: Graph spanners. Journal of Graph Theory 13(1), 99–116 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Keil, J.M., Gutwin, C.A.: Classes of graphs which approximate the complete euclidean graph. Discrete Computational Geometry 7, 13–28 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Pinchasi, R., Smorodinksy, S.: On the delaunay graph of a geometric graph. In: ACM Symposium on Computational Geometry - SoCG 2004, Brooklyn, NY (2004)Google Scholar
  10. 10.
    Kuratowski, K.: Sur le problème des courbes gauches en topologie. Fundamental Mathematics 15, 271–283 (1930)zbMATHGoogle Scholar
  11. 11.
    Bose, P., Morin, P., Stojmenovic, I., Urrutia, J.: Routing with guaranteed delivery in ad hoc wireless networks. wireless networks 7(6), 609–616 (2001)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Mark D. Watson
    • 1
  • J. Mark Keil
    • 1
  1. 1.Department of Computer ScienceUniversity of SaskatchewanCanada

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