Covering algorithms, continuum percolation and the geometry of wireless networks

DOI10.1214/aoap/1050689601zbMath1029.60077OpenAlexW1976464463MaRDI QIDQ1413688

Massimo Franceschetti, Jehoshua Bruck, Lorna Booth, Ronald W. J. Meester

Publication date: 17 November 2003

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aoap/1050689601

zbMATH Keywords

point processcontinuum percolationconnected componentcovering algorithm

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Circuits, networks (94C99) Percolation (82B43)

Related Items (6)

The spectrum of a random geometric graph is concentrated ⋮ Maximizing system lifetime in wireless sensor networks ⋮ Designing a contact process: the piecewise-homogeneous process on a finite set with applications ⋮ Monotone properties of random geometric graphs have sharp thresholds ⋮ Continuum percolation with unreliable and spread-out connections ⋮ Connectivity in finite ad-hoc networks

Cites Work

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• On continuum percolation
• Uniqueness of unbounded occupied and vacant components in Boolean models
• The longest edge of the random minimal spanning tree
• Probability theory of classical Euclidean optimization problems
• Supercritical contact processes on Z
• The Russo-Seymour-Welsh theorem and the equality of critical densities and the ``dual critical densities for continuum percolation on \({\mathbb{R}}^ 2\)
• On the strength of connectedness of a random graph
• Random Plane Networks
• The capacity of wireless networks
• Nearest neighbor and hard sphere models in continuum percolation

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