### Abstract

We consider centralized deterministic broadcasting in radio networks. The aim is to design a polynomial algorithm, which, given a graph G, produces a fast broadcasting scheme in the radio network represented by G. The problem of finding an optimal broadcasting scheme for a given graph is NP-hard, hence we can only hope for a good approximation algorithm. We give a deterministic polynomial algorithm which produces a broadcasting scheme working in time O(D log n + log^{2} n), for every n-node graph of diameter D. It has been proved recently [15, 16] that a better order of magnitude of broadcasting time is impossible unless NP ⊆ BPTIME(n^{o(log log n)}). In terms of approximation ratio, we have a O(log(n/D))-approximation algorithm for the radio broadcast problem, whenever D = Ω(log n).

Original language | English (US) |
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Pages (from-to) | 171-182 |

Number of pages | 12 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 3122 |

Publication status | Published - Dec 1 2004 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)