## Abstract

The paper concerns time-efficient k-shot broadcasting in undirected radio networks. In a k-shot broadcasting algorithm, each node in the network is allowed to transmit at most k times. Both known and unknown topology models are considered. For the known topology model, the problem has been studied before by Ga̧sieniec et al. [14], who established an upper bound of D+O(kn ^{1/(k-2)}log^{2} n) and a lower bound of on the length of k-shot broadcasting schedules for n-node graphs of diameter D. We improve both the upper and the lower bound, providing a randomized algorithm for constructing a k-shot broadcasting schedule of length D+O(kn ^{1/2k} log ^{2+1/k} n) on undirected graphs, and a lower bound of , which almost closes the gap between these bounds. For the unknown topology model, we provide the first k-shot broadcasting algorithm. Assuming that each node knows only the network size n (or a linear upper bound on it), our randomized k-shot broadcasting algorithm completes broadcasting in O((D+min {D •k,logn}) •n ^{1/(k-1)}logn) rounds with high probability. Moreover, we present an -shot broadcasting algorithm that completes broadcasting in at most O(Dlogn+log^{2} n) rounds with high probability. This algorithm matches the broadcasting time of the algorithm of Bar-Yehuda et al. [3], which assumes no limitation on the maximum number of transmissions per node.

Original language | English |
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Title of host publication | Distributed Computing - 23rd International Symposium, DISC 2009, Proceedings |

Pages | 481-495 |

Number of pages | 15 |

DOIs | |

State | Published - 2009 |

Externally published | Yes |

Event | 23rd International Symposium on Distributed Computing, DISC 2009 - Elche, Spain Duration: 23 Sep 2009 → 25 Sep 2009 |

### 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 | 5805 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 23rd International Symposium on Distributed Computing, DISC 2009 |
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Country/Territory | Spain |

City | Elche |

Period | 23/09/09 → 25/09/09 |

### Bibliographical note

Funding Information:Supported in part by grants from the Minerva Foundation and the Israel Ministry of Science.