## 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 κ-connectivity is the smallest r such that if all nodes have the transmission radius r, the induced topology is κ-connected. In this paper, we study the asymptotic critical transmission radius for κ -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 κ-connectivity. In addition, the critical neighbor number for κ-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 (symmetric) topology is κ-connected. Applying the critical transmission radius for κ-connectivity, we can obtain an asymptotic almost sure upper bound on the critical neighbor number for κ-connectivity.

Original language | English |
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Article number | 2046254 |

Pages (from-to) | 2867-2874 |

Number of pages | 8 |

Journal | IEEE Transactions on Information Theory |

Volume | 56 |

Issue number | 6 |

DOIs | |

State | Published - 1 Jun 2010 |

## Keywords

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