A Strong Zero-One Law for Connectivity in One-Dimensional Geometric Random Graphs With Non-Vanishing Densities

Abstract

We consider the geometric random graph where n points are distributed independently on the unit interval [0, 1] according to some probability distribution function F. Two nodes communicate with each other if their distance is less than some transmission range. When F admits a continuous density f which is strictly positive on [0, 1], we show that the property of graph connectivity exhibits a strong critical threshold and we identify it. This is achieved by generalizing a limit result on maximal spacings due to Levy for the uniform distribution.

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Document Details

Document Type
Technical Report
Publication Date
Apr 30, 2007
Accession Number
ADA468079

Entities

People

  • Armand M. Makowski
  • Guang Han

Organizations

  • University of Maryland

Tags

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  • C4I

DTIC Thesaurus Topics

  • Abstracts
  • Convergence
  • Distribution Functions
  • Electronic Mail
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Fields of Study

  • Mathematics

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  • Computer Networking
  • Mathematical Modeling and Probability Theory.
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  • Space