### Abstract

We consider the gossip problem in a synchronous message-passing system. Participating processors are prone to omission failures, that is, a faulty processor may fail to send or receive a message. The gossip problem in the fault-tolerant setting is defined as follows: every correct processor must learn the initial value of any other processor, unless the other one is faulty; in the latter case either the initial value or the information about the fault must be learned. We develop two efficient algorithms that solve the gossip problem in time O (log n), where n is the number of processors in the system. The first one is an explicit algorithm (i.e., constructed in polynomial time) sending O (n log n + f^{2}) messages, and the second one reduces the message complexity to O (n + f^{2}), where f is the upper bound on the number of faulty processors.

Original language | English (US) |
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Pages (from-to) | 308-314 |

Number of pages | 7 |

Journal | Information Processing Letters |

Volume | 109 |

Issue number | 6 |

DOIs | |

Publication status | Published - Feb 28 2009 |

Externally published | Yes |

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### Keywords

- Algorithms
- Distributed computing
- Fault tolerance
- Gossip problem
- Omission failures

### ASJC Scopus subject areas

- Theoretical Computer Science
- Signal Processing
- Information Systems
- Computer Science Applications

### Cite this

*Information Processing Letters*,

*109*(6), 308-314. https://doi.org/10.1016/j.ipl.2007.11.022