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Probabilistic bounds on the length of a longest edge in Delaunay graphs of random points in d-dimensions

Arkin, Esther M. and Fernández Anta, Antonio and Mitchell, Joseph S. B. and Mosteiro, Miguel A. (2015) Probabilistic bounds on the length of a longest edge in Delaunay graphs of random points in d-dimensions. [Journal Articles]

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Abstract

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.

Item Type: Journal Articles
Uncontrolled Keywords: Multidimensional Delaunay Graphs, Random Geometric Graph s, Radio Networks.
Subjects: UNSPECIFIED
Divisions: UNSPECIFIED
Depositing User: Antonio Fernandez
Date Deposited: 13 Mar 2015 13:10
Last Modified: 30 Nov 2016 11:59
URI: http://eprints.networks.imdea.org/id/eprint/996

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