Document Type

Article

Publication Date

9-2013

Abstract

The secrecy graph is a random geometric graph which is intended to model the connectivity of wireless networks under secrecy constraints. Directed edges in the graph are present whenever a node can talk to another node securely in the presence of eavesdroppers, which, in the model, is determined solely by the locations of the nodes and eavesdroppers. In the case of infinite networks, a critical parameter is the maximum density of eavesdroppers that can be accommodated while still guaranteeing an infinite component in the network, i.e., the percolation threshold. We focus on the case where the locations of the nodes and eavesdroppers are given by Poisson point processes, and present bounds for different types of percolation, including in-, out- and undirected percolation.

Publication Title

Discrete Applied Mathematics

Volume

161

Issue

13-14

First Page

2120

Last Page

2132

Required Publisher's Statement

Copyright © 2013 Elsevier B.V.

DOI:10.1016/j.dam.2013.03.022

Comments

This is the authors' version of the article. The publisher version is available here: http://www.sciencedirect.com/science/article/pii/S0166218X13001698

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Mathematics Commons

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