Distributed Averaging Via Lifted Markov Chains

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Motivated by applications of distributed linear estimation, distributed control, and distributed optimization, we consider the question of designing linear iterative algorithms for computing the average of numbers in a network. Specifically, our interest is in designing such an algorithm with the fastest rate of convergence given the topological constraints of the network. As the main result of this paper, we design an algorithm with the fastest possible rate of convergence using a nonreversible Markov chain on the given network graph. We construct such a Markov chain by transforming the standard Markov chain, which is obtained using the Metropolis-Hastings method. We call this novel transformation pseudo-lifting. We apply our method to graphs with geometry, or graphs with doubling dimension. Specifically, the convergence time of our algorithm (equivalently, the mixing time of our Markov chain) is proportional to the diameter of the network graph and hence optimal. As a byproduct, our result provides the fastest mixing Markov chain given the network topological constraints, and should naturally find their applications in the context of distributed optimization, estimation and control.
Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Issue Date
2010-01
Language
English
Article Type
Article
Keywords

WALK

Citation

IEEE TRANSACTIONS ON INFORMATION THEORY, v.56, no.1, pp.634 - 647

ISSN
0018-9448
DOI
10.1109/TIT.2009.2034777
URI
http://hdl.handle.net/10203/21839
Appears in Collection
CS-Journal Papers(저널논문)EE-Journal Papers(저널논문)
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