On the Zero-One Laws for Connectivity in One-Dimensional Geometric Random Graphs

Abstract

We consider the geometric random graph where n points are distributed uniformly and independently on the unit interval [0, 1]. Using the method of first and second moments, we provide a simple proof of the ?zero-one? law for the property of graph connectivity under the asymptotic regime created by having n become large and the transmission range scaled appropriately with n.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2006
Accession Number
ADA604697

Entities

People

  • Armand M. Makowski
  • Guang Han

Organizations

  • University of Maryland

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Boundaries
  • Computers
  • Engineering
  • Information Operations
  • Intervals
  • Literature
  • Maryland
  • Observation
  • Phase Transformations
  • Probability
  • Transitions
  • Universities

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Graph Algorithms and Convex Optimization.