Probabilistic connectivity threshold for directional antenna widths

Hadassa Daltrophe, Shlomi Dolev, Zvi Lotker

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Consider the task of maintaining connectivity in a wireless network where the network nodes are equipped with directional antennas. Nodes correspond to points on the unit disk and each uses a directional antenna covering a sector of a given angle α, where the orientation of the sector is either random or not. The width required for a connectivity problem is to find out the necessary and sufficient conditions of α that guarantee connectivity when an antenna's location is uniformly distributed and the direction is either random or not. We prove basic and fundamental results about this (reformulated) problem. We show that when the number of network nodes is big enough, the required α approaches zero. Specifically, on the unit disk it holds with high probability that the threshold for connectivity α = Θ (4√log n/n. This is shown by the use of Poisson approximation and geometrical considerations. Moreover, when the model is relaxed to allow orientation towards the center of the area, we demonstrate that α = Θ (log n/n) is a necessary and sufficient condition.

Original languageEnglish
Title of host publicationStructural Information and Communication Complexity - 20th International Colloquium, SIROCCO 2013, Revised Selected Papers
Pages225-236
Number of pages12
DOIs
StatePublished - 1 Dec 2013
Event20th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2013 - Ischia, Italy
Duration: 1 Jul 20133 Jul 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8179 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference20th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2013
Country/TerritoryItaly
CityIschia
Period1/07/133/07/13

Keywords

  • Connectivity threshold
  • Directional antennas
  • Wireless networks

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