Degree Fluctuations and the Convergence Time of Consensus Algorithms
Name
P-12-ao-degree-fluct-final.pdf
Description
Accepted version
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558.62 KB
Format
Adobe PDF
Checksum (MD5)
208359adc16f6a26236aaedea3374a08
Author(s)
Olshevsky, Alex
Tsitsiklis, John N
Date Issued
2013
Journal
IEEE Transactions on Automatic Control
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Version
Author's final manuscript
Abstract
We consider a consensus algorithm in which every nodein a sequence of undirected, B-connected graphs assigns equal weight to each of its neighbors. Under the assumption that the degree of each node is fixed (except for times when the node has no connections to other nodes), we show that consensus is achieved within a given accuracy on nodes in time B+4n3In(2n/ε). Because there is a direct relation between consensus algorithms in time-varying environments and in homogeneous random walks, our result also translates into a general statement on such random walks.Moreover, we give a simple proof of a result of Cao, Spielman, and Morse that the worst case convergence time becomes exponentially large inthe number of nodes under slight relaxation of the degree constancy assumption. ©2013 IEEE.
MIT Department
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/TAC.2013.2257969
