### 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 language | English |
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Pages | 1-8 |

Number of pages | 8 |

State | Published - 20 Sep 2004 |

Event | Proceedings of the Fifth ACM International Symposium on Mobile Ad Hoc Networking and Computing, MoBiHoc 2004 - Tokyo, Japan Duration: 24 May 2004 → 26 May 2004 |

### Conference

Conference | Proceedings of the Fifth ACM International Symposium on Mobile Ad Hoc Networking and Computing, MoBiHoc 2004 |
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Country | Japan |

City | Tokyo |

Period | 24/05/04 → 26/05/04 |

### Keywords

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

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## Cite this

*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.