### Abstract

We study here the gossiping problem (all-to-all communication) in known radio networks, i.e., when all nodes are aware of the network topology. We start our presentation with a deterministic algorithm for the gossiping problem that works in at most n units of time in any radio network of size n. This is an optimal algorithm in the sense that there exist radio network topologies, such as: a line, a star and a complete graph in which the radio gossiping cannot be completed in less then n units of time. Furthermore, we show that there isn't any radio network topology in which the gossiping task can be solved in time < ⌊log(n - 1)⌋ + 2. We show also that this lower bound can be matched from above for a fraction of all possible integer values of n; and for all other values of n we propose a solution admitting gossiping in time ⌈log(n - 1)⌉ + 2. Finally we study asymptotically optimal O(D)-time gossiping (where D is a diameter of the network) in graphs with max-degree Δ = O(D^{1-1/(i+1)}/ log^{i} n), for any integer constant i ≥ 0 and D large enough.

Original language | English (US) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Editors | Rastislav Kralovic, Ondrej Sykora |

Publisher | Springer Verlag |

Pages | 173-184 |

Number of pages | 12 |

ISBN (Print) | 3540222308 |

DOIs | |

State | Published - Jan 1 2004 |

Externally published | Yes |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 3104 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(pp. 173-184). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3104). Springer Verlag. https://doi.org/10.1007/978-3-540-27796-5_16