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On the expected maximum degree of Gabriel and Yao graphs

Part of: Discrete geometry Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Luc Devroye ,
Joachim Gudmundsson  and
Pat Morin
Luc Devroye*
Affiliation:
McGill University
Joachim Gudmundsson*
Affiliation:
NICTA
Pat Morin*
Affiliation:
Carleton University
*
∗ Postal address: School of Computer Science, McGill University, 3480 University Street, Montreal, Québec, H3A 2A7, Canada.
∗∗ Postal address: NICTA, School of IT Building, J12 1 Cleveland Street, University of Sydney, NSW 2006, Australia.
∗∗∗ Postal address: School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, K1S 5B6, Canada.
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Abstract

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Motivated by applications of Gabriel graphs and Yao graphs in wireless ad-hoc networks, we show that the maximum degree of a random Gabriel graph or Yao graph defined on n points drawn uniformly at random from a unit square grows as Θ (log n / log log n) in probability.

Keywords

Random geometric graphGabriel graphYao graphmaximum degree

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 68U05: Computer graphics; computational geometry 52C99: None of the above, but in this section
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 41 , Issue 4 , December 2009 , pp. 1123 - 1140
Copyright
Copyright © Applied Probability Trust 2009 

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