On the expected maximum degree of Gabriel and Yao graphs

On the expected maximum degree of Gabriel and Yao graphs

Luc Devroye, Joachim Gudmundsson, and Pat Morin

Source: Adv. in Appl. Probab. Volume 41, Number 4 (2009), 1123-1140.

Abstract

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.

First Page: Show

Primary Subjects: 60D05

Secondary Subjects: 68U05, 52C99

Keywords: Random geometric graph; Gabriel graph; Yao graph; maximum degree

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Permanent link to this document: http://projecteuclid.org/euclid.aap/1261669589
Digital Object Identifier: doi:10.1239/aap/1261669589
Zentralblatt MATH identifier: 05706693
Mathematical Reviews number (MathSciNet): MR2663239

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