### Abstract

We consider the gossiping problem in the classical random phone-call model introduced by Demers et. al. ([6]). We are given a complete graph, in which every node has an initial message to be disseminated to all other nodes. In each step every node is allowed to establish a communication channel with a randomly chosen neighbour. Karp et al. [15] proved that it is possible to design a randomized procedure performing O(nloglogn) transmissions that accomplishes broadcasting in time O(logn), with probability 1-n ^{-}1. In this paper we provide a lower bound argument that proves Ω(nlogn) message complexity for any O(logn)-time randomized gossiping algorithm, with probability 1-o(1). This should be seen as a separation result between broadcasting and gossiping in the random phone-call model. We study gossiping at the two opposite points of the time and message complexity trade-off. We show that one can perform gossiping based on exchange of O(n•logn/loglogn) messages in time O(log^{2} n/loglogn), and based on exchange of O(nloglogn) messages with the time complexity Both results hold wit probability 1-n ^{-1}. Finally, we consider a model in which each node is allowed to store a small set of neighbours participating in its earlier transmissions. We show that in this model randomized gossiping based on exchange of O(nloglogn) messages can be obtained in time O(logn), with probability 1-n ^{-1}.

Original language | English (US) |
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Title of host publication | Automata, Languages and Programming - 37th International Colloquium, ICALP 2010, Proceedings |

Pages | 127-138 |

Number of pages | 12 |

Edition | PART 2 |

DOIs | |

State | Published - Aug 12 2010 |

Externally published | Yes |

Event | 37th International Colloquium on Automata, Languages and Programming, ICALP 2010 - Bordeaux, France Duration: Jul 6 2010 → Jul 10 2010 |

### 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 | 6199 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 37th International Colloquium on Automata, Languages and Programming, ICALP 2010 |
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Country | France |

City | Bordeaux |

Period | 7/6/10 → 7/10/10 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Automata, Languages and Programming - 37th International Colloquium, ICALP 2010, Proceedings*(PART 2 ed., pp. 127-138). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6199 LNCS, No. PART 2). https://doi.org/10.1007/978-3-642-14162-1_11