### Abstract

We consider broadcasting with a linearly bounded number of transmission failures. For a constant parameter 0 < α < 1 we assume that at most αi faulty transmissions can occur during the first i time units of the communication process, for every natural number i. Every informed node can transmit information to at most one neighbor in a unit of time. Faulty transmissions have no effect. We investigate worst-case optimal non-adaptive broadcasting time under this fault model, for several communication networks. We show, e.g., that for the n-node line network this time is linear in n, if α < 1/2, and exponential otherwise. For the hypercube and the complete graph, broadcasting in the linearly bounded fault model can be performed in time logarithmic in the number of nodes.

Original language | English (US) |
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Pages (from-to) | 121-133 |

Number of pages | 13 |

Journal | Discrete Applied Mathematics |

Volume | 83 |

Issue number | 1-3 |

DOIs | |

State | Published - Mar 25 1998 |

Externally published | Yes |

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

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## Cite this

*Discrete Applied Mathematics*,

*83*(1-3), 121-133. https://doi.org/10.1016/S0166-218X(97)00107-8