2011/06/24 by Esther M. Arkin, Antonio Fernández Anta, Arkin, Esther M. +6
Computer Science · Mathematics · #05C10 #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #Discrete Mathematics (cs.DM) #F.2.2 #FOS: Computer and information sciences #G.2.2 #Mobile Ad Hoc Networks #Stochastic processes and statistical mechanics #acm:05C10 #cs.CG #cs.DM #msc:05C10
paper · pdf · doi:10.48550/arxiv.1106.4927
10 pages. 2 figures. In Proceedings of the 23rd Canadian Conference on Computational Geometry (CCCG 2011). Replacement of version 1106.4927, reference [5] added
openalex publication_date 2011/06/24 · arxiv created 2011/08/22 · arxiv updated 2011/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by low energy consumption in geographic routing in wireless networks, there has been recent interest in determining bounds on the length of edges in the Delaunay graph of randomly distributed points. Asymptotic results are known for random networks in planar domains. In this paper, we obtain upper and lower bounds that hold with parametric probability in any dimension, for points distributed uniformly at random in domains with and without boundary. The results obtained are asymptotically tight for all relevant values of such probability and constant number of dimensions, and show that the overhead produced by boundary nodes in the plane holds also for higher dimensions. To our knowledge, this is the first comprehensive study on the lengths of long edges in Delaunay graphs