Order optimal information spreading using algebraic gossip

Chen Avin, Michael Borokhovich, Keren Censor-Hillel, Zvi Lotker

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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 (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.

Original languageEnglish
Pages (from-to)99-117
Number of pages19
JournalDistributed Computing
Volume26
Issue number2
DOIs
StatePublished - 1 Apr 2013

Keywords

  • Algebraic Gossip
  • Conductance
  • Gossip algorithms
  • Information spreading
  • Network capacity
  • Network coding

Fingerprint

Dive into the research topics of 'Order optimal information spreading using algebraic gossip'. Together they form a unique fingerprint.

Cite this