## Abstract

In this paper we study gossip based information spreading with bounded message sizes. We use algebraic gossip to disseminate k distinct messages to all n nodes in a network. For arbitrary networks we provide a new upper bound for uniform algebraic gossip of O((k + log n + D)Δ) rounds with high probability, where D and Δ are the diameter and the maximum degree in the network, respectively. For many topologies and selections of k this bound improves previous results, in particular, for graphs with a constant maximum degree it implies that uniform gossip is order optimal and the stopping time is θ(k + D). To eliminate the factor of Δ from the upper bound we propose a non-uniform gossip protocol, TAG, which is based on algebraic gossip and an arbitrary spanning tree protocol S. The stopping time of TAG is O(k+ log n + d(S) + t(S)), where t(S) is the stopping time of the spanning tree protocol, and d(S) is the diameter of the spanning tree. We provide two general cases in which this bound leads to an order optimal protocol. The first is for k=Ω(n), where, using a simple gossip broadcast protocol that creates a spanning tree in at most linear time, we show that TAG finishes after θ(n) rounds for any graph. The second uses a sophisticated, recent gossip protocol to build a fast spanning tree on graphs with large weak conductance. In turn, this leads to the optimally of TAG on these graphs for k=Ω(polylog(n)). The technique used in our proofs relies on queuing theory, which is an interesting approach that can be useful in future gossip analysis.

Original language | English |
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Title of host publication | PODC'11 - Proceedings of the 2011 ACM Symposium Principles of Distributed Computing |

Pages | 363-371 |

Number of pages | 9 |

DOIs | |

State | Published - 7 Jul 2011 |

Event | 30th Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC'11, Held as Part of the 5th Federated Computing Research Conference, FCRC - San Jose, CA, United States Duration: 6 Jun 2011 → 8 Jun 2011 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Principles of Distributed Computing |
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### Conference

Conference | 30th Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC'11, Held as Part of the 5th Federated Computing Research Conference, FCRC |
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Country/Territory | United States |

City | San Jose, CA |

Period | 6/06/11 → 8/06/11 |

## Keywords

- algebraic gossip
- gossip
- network coding
- tight bounds

## ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Computer Networks and Communications