The match-maker: Constant-space distributed majority via random walks

Leszek Gąsieniec, David D. Hamilton, Russell Martin, Paul G. Spirakis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

We propose and analyze here a simple protocol for consensus on the majority color in networks whose nodes are initially one of two colors. Our protocol guarantees that, if a majority exists, then eventually each node learns of the majority color. Our protocol requires only 2 bits of memory per node and uses a simple token message, of also 2 bits size, that performs random walks. We show correctness of our protocol for any connected graph (even unknown to the nodes) and even for a natural class of dynamic graphs. We show upper and lower bounds on the convergence time of our protocol.We discuss termination and we also provide a variant of our protocol which the token uses a counter that can count only up to √n log n, where n is the number of network nodes. Our basic (memoryless) protocol takes only O(n log n) expected time on the clique which surprisingly does not deviate from the cover time of the random walk, and O(n2m) time on any connected undirected network of m edges and this bound is met from below by an argument on the line. Finally, we also consider random walks that can count the difference of colors and we show upper bounds on the counter value by using coupling arguments.

Original languageEnglish (US)
Title of host publicationStabilization, Safety and Security of Distributed Systems - 17th International Symposium, SSS 2015, Proceedings
EditorsAndrzej Pelc, Alexander A. Schwarzmann
PublisherSpringer Verlag
Pages67-80
Number of pages14
ISBN (Print)9783319217406
DOIs
StatePublished - Jan 1 2015
Externally publishedYes
Event17th International Symposium on Stabilization, Safety and Security of Distributed Systems, SSS 2015 - Edmonton, Canada
Duration: Aug 18 2015Aug 21 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9212
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other17th International Symposium on Stabilization, Safety and Security of Distributed Systems, SSS 2015
CountryCanada
CityEdmonton
Period8/18/158/21/15

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Gąsieniec, L., Hamilton, D. D., Martin, R., & Spirakis, P. G. (2015). The match-maker: Constant-space distributed majority via random walks. In A. Pelc, & A. A. Schwarzmann (Eds.), Stabilization, Safety and Security of Distributed Systems - 17th International Symposium, SSS 2015, Proceedings (pp. 67-80). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9212). Springer Verlag. https://doi.org/10.1007/978-3-319-21741-3_5