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Distributed Computing

, Volume 26, Issue 2, pp 99–117 | Cite as

Order optimal information spreading using algebraic gossip

  • Chen Avin
  • Michael Borokhovich
  • Keren Censor-Hillel
  • Zvi Lotker
Article

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 \(O((k+\log n + D)\varDelta )\) rounds with high probability, where \(D\) and \(\varDelta \) 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 \(\varTheta (k + D)\). To eliminate the factor of \(\varDelta \) from the upper bound we propose a non-uniform gossip protocol, TAG, which is based on algebraic gossip and an arbitrary spanning tree protocol \(\mathcal{S } \). The stopping time of TAG is \(O(k+\log n +d(\mathcal{S })+t(\mathcal{S }))\), where \(t(\mathcal{S })\) is the stopping time of the spanning tree protocol, and \(d(\mathcal{S })\) 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 \(k=\varOmega (n)\), where, using a simple gossip broadcast protocol that creates a spanning tree in at most linear time, we show that TAG finishes after \(\varTheta (n)\) 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 \(k=\varOmega (\text{ polylog }(n))\). The technique used in our proofs relies on queuing theory, which is an interesting approach that can be useful in future gossip analysis.

Keywords

Algebraic Gossip Gossip algorithms Network capacity Network coding Information spreading Conductance 

Notes

Acknowledgments

Keren Censor-Hillel was partially supported by NSF Award 0939370-CCF. Zvi Lotker and Michael Borokhovich were supported in part by a grant from the Israel Science Foundation (894/09). We would like to thank the anonymous reviewers who helped us to significantly improve the paper.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Chen Avin
    • 1
  • Michael Borokhovich
    • 1
  • Keren Censor-Hillel
    • 2
  • Zvi Lotker
    • 1
  1. 1.Department of Communication Systems EngineeringBen Gurion UniversityBeer-ShevaIsrael
  2. 2.Computer Science and Artificial Intelligence LaboratoryMITCambridgeUSA

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