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CORR
2011
Springer

Degree Fluctuations and the Convergence Time of Consensus Algorithms

8 years 7 days ago
Degree Fluctuations and the Convergence Time of Consensus Algorithms
We consider a consensus algorithm in which every node in a time-varying undirected connected graph assigns equal weight to each of its neighbors. Under the assumption that the degree of any given node is constant in time, we show that the algorithm achieves consensus within a given accuracy in time O(n3 ln(n/ )). Because there is a direct relation between consensus algorithms in time-varying environments and inhomogeneous random walks, our result also translates into a general statement on such random walks. Moreover, we give simple proofs that the convergence time becomes exponential under slight relaxations of the above assumptions. We prove that exponential convergence time is possible for consensus algorithms on fixed directed graphs, and we use an example of Cao, Spielman, and Morse to give a simple argument that the same is possible if the constant degrees assumption is even slightly relaxed.
Alexander Olshevsky, John N. Tsitsiklis
Added 13 May 2011
Updated 13 May 2011
Type Journal
Year 2011
Where CORR
Authors Alexander Olshevsky, John N. Tsitsiklis
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