Tight bounds for algebraic gossip on graphs

Michael Borokhovich, Chen Avin, Zvi Lotker

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

29 Scopus citations

Abstract

We study the stopping times of gossip algorithms for network coding. We analyze algebraic gossip (i.e., random linear coding) and consider three gossip algorithms for information spreading Pull, Push, and Exchange. The stopping time of algebraic gossip is known to be linear for the complete graph, but the question of determining a tight upper bound or lower bounds for general graphs is still open. We take a major step in solving this question, and prove that algebraic gossip on any graph of size n is O(Δn) where Δ is the maximum degree of the graph. This leads to a tight bound of θ(n) for bounded degree graphs and an upper bound of O(n2) for general graphs. We show that the latter bound is tight by providing an example of a graph with a stopping time of Ω (n2). Our proofs use a novel method that relies on Jackson's queuing theorem to analyze the stopping time of network coding; this technique is likely to become useful for future research.

Original languageEnglish
Title of host publication2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings
Pages1758-1762
Number of pages5
DOIs
StatePublished - 23 Aug 2010
Event2010 IEEE International Symposium on Information Theory, ISIT 2010 - Austin, TX, United States
Duration: 13 Jun 201018 Jun 2010

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8103

Conference

Conference2010 IEEE International Symposium on Information Theory, ISIT 2010
Country/TerritoryUnited States
CityAustin, TX
Period13/06/1018/06/10

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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