Asymptotic critical transmission radius and critical neighbor number for k-connectivity in wireless ad hoc networks

Peng Jun Wan*, Tsi-Ui Ik

*Corresponding author for this work

Research output: Contribution to conferencePaper

107 Scopus citations

Abstract

A range assignment to the nodes in a wireless ad hoc network induces a topology in which there is an edge between two nodes if and only if both of them are within each other's transmission range. The critical transmission radius for k-connectivity is the smallest r such that if all nodes have the transmission radius r, the induced topology is k-connected. The critical neighbor number for k-connectivity is the smallest integer l such that if every node sets its transmission radius equal to the distance between itself and its l-th nearest neighbor, the induced topology is k-connected. In this paper, we study the asymptotic critical transmission radius for k-connectivity and asymptotic critical neighbor number for k-connectivity in a wireless ad hoc network whose nodes are uniformly and independently distributed in a unit-area square or disk. We provide a precise asymptotic distribution of the critical transmission radius for k-connectivity and an improved asymptotic almost sure upper bound on the critical neighbor number for k-connectivity.

Original languageEnglish
Pages1-8
Number of pages8
StatePublished - 20 Sep 2004
EventProceedings of the Fifth ACM International Symposium on Mobile Ad Hoc Networking and Computing, MoBiHoc 2004 - Tokyo, Japan
Duration: 24 May 200426 May 2004

Conference

ConferenceProceedings of the Fifth ACM International Symposium on Mobile Ad Hoc Networking and Computing, MoBiHoc 2004
CountryJapan
CityTokyo
Period24/05/0426/05/04

Keywords

  • Asymptotic distribution
  • Critical neighbor number
  • Critical transmission radius
  • Random geometric graph

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    Wan, P. J., & Ik, T-U. (2004). Asymptotic critical transmission radius and critical neighbor number for k-connectivity in wireless ad hoc networks. 1-8. Paper presented at Proceedings of the Fifth ACM International Symposium on Mobile Ad Hoc Networking and Computing, MoBiHoc 2004, Tokyo, Japan.