CONVERGENCE SPEED IN DISTRIBUTED CONSENSUS AND AVERAGING

We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a consensus algorithm leads to an averaging algorithm. We prove...

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Bibliographic Details
Published inSIAM journal on control and optimization Vol. 48; no. 1; p. 33
Main Authors Olshevsky, Alex, Tsitsiklis, John N
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2009
Subjects
Adaptation
Algorithms
Communications networks
Convergence
Distributed processing
Iterative algorithms
Lower bounds
Network topologies
Optimization
Studies
Topology
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Summary:We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a consensus algorithm leads to an averaging algorithm. We prove lower bounds on the worst-case convergence time for various classes of linear, time-invariant, distributed consensus methods, and provide an algorithm that essentially matches those lower bounds. We then consider the case of a time-varying topology, and provide a polynomial-time averaging algorithm. [PUBLICATION ABSTRACT]
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ISSN:0363-0129
1095-7138
DOI:10.1137/060678324