### Abstract

We present new distributed deterministic solutions to two communication problems in n-node ad-hoc radio networks: rumor gathering and multi-broadcast. In these problems, some or all nodes of the network initially contain input data called rumors, which have to be learned by other nodes. In rumor gathering, there are k rumors initially distributed arbitrarily among the nodes, and the goal is to collect all the rumors at one node. Our rumor gathering algorithm works in O((k + n)log n) time and our multi-broadcast algorithm works in O(k log^{3} n + n log^{4} n) time, for any n-node networks and k rumors (with arbitrary k), which is a substantial improvement over the best previously known deterministic solutions to these problems. As a consequence, we exponentially decrease the gap between upper and lower bounds on the deterministic time complexity of four communication problems: rumor gathering, multi-broadcast, gossiping and routing, in the important case when every node has initially at most one rumor (this is the scenario for gossiping and for the usual formulation of routing). Indeed, for k = O(n), our results simultaneously decrease the complexity gaps for these four problems from polynomial to polylogarithmic in the size of the graph. Moreover, our deterministic gathering algorithm applied for k = O(n) rumors, improves over the best previously known randomized algorithm of time O(k log n + n log^{2} n).

Original language | English (US) |
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Title of host publication | Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings |

Pages | 613-624 |

Number of pages | 12 |

Edition | PART 2 |

DOIs | |

State | Published - Jul 11 2011 |

Externally published | Yes |

Event | 38th International Colloquium on Automata, Languages and Programming, ICALP 2011 - Zurich, Switzerland Duration: Jul 4 2011 → Jul 8 2011 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Number | PART 2 |

Volume | 6756 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 38th International Colloquium on Automata, Languages and Programming, ICALP 2011 |
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Country | Switzerland |

City | Zurich |

Period | 7/4/11 → 7/8/11 |

### Keywords

- distributed algorithm
- gathering
- gossiping
- multi-broadcast
- radio network
- routing

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings*(PART 2 ed., pp. 613-624). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6756 LNCS, No. PART 2). https://doi.org/10.1007/978-3-642-22012-8_49