## Abstract

The paper concerns time-efficient k-shot broadcasting in undirected radio networks for n-node graphs of diameter D. 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 Gaąsieniec et al. (2008). We improve both the upper and the lower bound of that paper providing a randomized algorithm for constructing a k-shot broadcasting schedule of length D+O(k^{n1/2k}^{log2+1/k}n) on undirected graphs, and a lower bound of D+Ω(kω^{(n-D)1/2k}), 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{Dωk,logn})ω^{n1/(k-1)}logn) rounds with high probability for k≥2, and in O(Dω^{n2}logn) rounds with high probability for k=1. Moreover, we present an Θ(logn)-shot broadcasting algorithm that completes broadcasting in at most O(Dlogn+^{log2}n) rounds with high probability. This algorithm matches the broadcasting time of the algorithm of Bar-Yehuda et al. (1992), which assumes no limitation on the maximum number of transmissions per node.

Original language | English |
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Pages (from-to) | 79-94 |

Number of pages | 16 |

Journal | Discrete Applied Mathematics |

Volume | 202 |

DOIs | |

State | Published - 31 Mar 2016 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2015 Elsevier B.V. All rights reserved.

### Funding

This work is partially supported by AFOSR FA9550-13-1-0042 and NSF grants Nos. CCF-0939370 , CCF-1217506 , and CCF-AF-0937274 and by a grant from the Israel Ministry of Science ( 36478 ).

Funders | Funder number |
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Israel Ministry of Science | 36478 |

National Science Foundation | CCF-0939370, CCF-1217506, CCF-AF-0937274 |

Air Force Office of Scientific Research | FA9550-13-1-0042 |

## Keywords

- Broadcasting
- Radio network
- Wireless network