Bounds for algebraic gossip on graphs

Michael Borokhovich, Chen Avin, Zvi Lotker

Research output: Contribution to journalArticlepeer-review

1 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
Pages (from-to)185-217
Number of pages33
JournalRandom Structures and Algorithms
Volume45
Issue number2
DOIs
StatePublished - 1 Jan 2014

Keywords

  • Algebraic gossip
  • Gossip
  • Gossip algorithms
  • Network capacity
  • Network coding

ASJC Scopus subject areas

  • Software
  • General Mathematics
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Bounds for algebraic gossip on graphs'. Together they form a unique fingerprint.

Cite this