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The Random Connection Model on the Torus

Published online by Cambridge University Press:  09 July 2014

LUC DEVROYE  and
NICOLAS FRAIMAN
LUC DEVROYE
Affiliation:
School of Computer Science, McGill University, Montreal, CanadaH3A 2K6 (e-mail: luc@cs.mcgill.ca)
NICOLAS FRAIMAN
Affiliation:
Department of Mathematics and Statistics, McGill University, Montreal, CanadaH3A 2K6 (e-mail: fraiman@math.mcgill.ca)
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Abstract

We study the diameter of a family of random graphs on the torus that can be used to model wireless networks. In the random connection model two points x and y are connected with probability g(y−x), where g is a given function. We prove that the diameter of the graph is bounded by a constant, which depends only on ‖g‖1, with high probability as the number of vertices in the graph tends to infinity.

Keywords

Primary 60C05Secondary 05C80
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 23 , Issue 5: Honouring the Memory of Philippe Flajolet - Part 1 , September 2014 , pp. 796 - 804
Copyright
Copyright © Cambridge University Press 2014 

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