On distributed averaging algorithms and quantization effects

Angelia Nedich, Alex Olshevsky, Asuman Ozdaglar, John N. Tsitsiklis

Research output: Contribution to journalArticle

320 Citations (Scopus)

Abstract

We consider distributed iterative algorithms for the averaging problem over time-varying topologies. Our focus is on the convergence time of such algorithms when complete (unquantized) information is available, and on the degradation of performance when only quantized information is available. We study a large and natural class of averaging algorithms, which includes the vast majority of algorithms proposed to date, and provide tight polynomial bounds on their convergence time. We also describe an algorithm within this class whose convergence time is the best among currently available averaging algorithms for time-varying topologies. We then propose and analyze distributed averaging algorithms under the additional constraint that agents can only store and communicate quantized information, so that they can only converge to the average of the initial values of the agents within some error. We establish bounds on the error and tight bounds on the convergence time, as a function of the number of quantization levels.

Original languageEnglish (US)
Article number5286289
Pages (from-to)2506-2517
Number of pages12
JournalIEEE Transactions on Automatic Control
Volume54
Issue number11
DOIs
StatePublished - Nov 2009
Externally publishedYes

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Parallel algorithms
Topology
Polynomials
Degradation

Keywords

  • Decentralized and distributed control
  • Multiagent systems

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Computer Science Applications

Cite this

On distributed averaging algorithms and quantization effects. / Nedich, Angelia; Olshevsky, Alex; Ozdaglar, Asuman; Tsitsiklis, John N.

In: IEEE Transactions on Automatic Control, Vol. 54, No. 11, 5286289, 11.2009, p. 2506-2517.

Research output: Contribution to journalArticle

Nedich, A, Olshevsky, A, Ozdaglar, A & Tsitsiklis, JN 2009, 'On distributed averaging algorithms and quantization effects', IEEE Transactions on Automatic Control, vol. 54, no. 11, 5286289, pp. 2506-2517. https://doi.org/10.1109/TAC.2009.2031203
Nedich, Angelia ; Olshevsky, Alex ; Ozdaglar, Asuman ; Tsitsiklis, John N. / On distributed averaging algorithms and quantization effects. In: IEEE Transactions on Automatic Control. 2009 ; Vol. 54, No. 11. pp. 2506-2517.
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