Geometrically aware communication in random wireless networks

Gady Kozma*, Zvi Lotker, Micha Sharir, Gideon Stupp

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review

13 Scopus citations


Some of the first routing algorithms for position-aware wireless networks used the Delaunay triangulation of the point-locations of the network's nodes as the underlying connectivity graph. Later on these solutions were considered impractical because the Delaunay triangulation may in general contain arbitrarily long edges and because calculating the Delaunay triangulation may require a global view of the network. Many other algorithms were then suggested for geometric routing, often assuming random placement of network nodes for analysis or simulation [27, 5, 28, 15]. But as we show, when the nodes are uniformly placed in the unit disk the Delaunay triangulation does not contain long edges, it is easy to compute locally and it is in many ways optimal for geometric routing and flooding. In particular, we prove that with high probability the maximal length of an edge in Del(P), the Delaunay triangulation of a set P of n nodes uniformly placed in the unit disk, is O (3√log n/n), and that the expected sum of squares of all the edges in Del(P) is O(1). These geometric results imply that for wireless networks, randomly distributed in a unit disk (1) computing the Delaunay triangulation locally is asymptotically easy; (2) simple "face routing" through the Delaunay triangulation optimizes, up to poly-logarithmic factors, the energy load on the nodes, and (3) flooding the network, an operation quite common in sensor nets, is with high probability optimal up to a constant factor. The last property is particularly important for geocasting because the Delaunay triangulation is known to be a spanner.

Original languageEnglish
Number of pages10
StatePublished - 2004
EventProceedings of the 23rd Annual ACM Symposium on Principles of Distributed Computing - St. John's, Nfld., Canada
Duration: 25 Jul 200428 Jul 2004


ConferenceProceedings of the 23rd Annual ACM Symposium on Principles of Distributed Computing
CitySt. John's, Nfld.


  • Delaunay triangulation
  • Geometric flooding
  • Geometric routing


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