On the Expected Maximum Degree of Gabriel and Yao Graphs

Luc Devroye; Joachim Gudmundsson; Pat Morin

On the Expected Maximum Degree of Gabriel and Yao Graphs

Computational Geometry 2009-05-25 v1 Distributed, Parallel, and Cluster Computing

Authors: Luc Devroye , Joachim Gudmundsson , Pat Morin

Abstract

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

Keywords

graph theory

Cite

@article{arxiv.0905.3584,
  title  = {On the Expected Maximum Degree of Gabriel and Yao Graphs},
  author = {Luc Devroye and Joachim Gudmundsson and Pat Morin},
  journal= {arXiv preprint arXiv:0905.3584},
  year   = {2009}
}

Comments

20 pages, 10 figures

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