## Abstract

Fault-tolerant broadcasting in the message passing and radio models is considered under a probabilistic failure model. At each step, the transmitter of each node may fail with fixed constant probability p < 1, and failures are independent. Both node-omission and malicious transmission failures are studied. Our goal is to establish conditions on feasibility and to estimate the (synchronous) time complexity of almost-safe broadcasting (i.e., broadcasting which is correct with probability at least 1 - 1 / n for n-node graphs and for sufficiently large n) under these scenarios. If only node-omission failures are assumed, almost-safe broadcasting is feasible for any p < 1, in both communication models. For malicious transmission failures, almost-safe broadcasting in the message passing model is feasible iff p < 1 / 2, and in the radio model it is feasible iff p < (1 - p)^{Δ + 1}, where Δ is the maximum degree of the network. For the time complexity of almost-safe broadcasting, a number of upper and lower bounds are given in the various models.

Original language | English |
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Pages (from-to) | 279-292 |

Number of pages | 14 |

Journal | Theoretical Computer Science |

Volume | 370 |

Issue number | 1-3 |

DOIs | |

State | Published - 12 Feb 2007 |

Externally published | Yes |

### Bibliographical note

Funding Information:The second author thanks Michael Brand for his helpful remarks. The first author was supported in part by NSERC discovery grant and by the Research Chair in Distributed Computing of the Université du Québec en Outaouais. Part of this research was done during the second author’s visit at the Research Chair in Distributed Computing of the Université du Québec en Outaouais.

### Funding

The second author thanks Michael Brand for his helpful remarks. The first author was supported in part by NSERC discovery grant and by the Research Chair in Distributed Computing of the Université du Québec en Outaouais. Part of this research was done during the second author’s visit at the Research Chair in Distributed Computing of the Université du Québec en Outaouais.

Funders | Funder number |
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Université du Québec en Outaouais | |

Natural Sciences and Engineering Research Council of Canada |

## Keywords

- Broadcasting
- Malicious transmission failures
- Message passing
- Node-omission failures
- Radio networks
- Random failures