### Abstract

We consider the problem of broadcasting in an n-node hypercube whose links and nodes fail independently with given probabilities p < 1 and q < 1, respectively. Information held in a fault-free node, called the source, has to reach all other fault-free nodes. Messages may be directly transmitted to adjacent nodes only, and every node may communicate with at most one neighbour in a unit of time. A message can be transmitted only if both communicating neighbours and the link joining them are fault-free. For parameters p and q satisfying (1 -p) (1-q) ≥ 0.99 (e.g. p = q = 0.5%), we give an algorithm working in time O (log n) and broadcasting source information to all fault-free nodes with probability exceeding 1- cn^{-ε} for some positive constant ε , c depending on p and q but not depending on n.

Original language | English (US) |
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Pages (from-to) | 337-350 |

Number of pages | 14 |

Journal | Combinatorics Probability and Computing |

Volume | 5 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jan 1 1996 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Statistics and Probability
- Computational Theory and Mathematics
- Applied Mathematics

### Cite this

*Combinatorics Probability and Computing*,

*5*(4), 337-350. https://doi.org/10.1017/S0963548300002108