Push-sum Algorithm on Time-varying Random Graphs
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In this thesis, we study the problem of achieving average consensus over a random time-varying sequence of directed graphs by extending the class of so-called push- sum algorithms to such random scenarios. Provided that an ergodicity notion, which we term the directed infinite flow property, holds and the auxiliary states of nodes are uniformly bounded away from zero infinitely often, we prove the almost sure convergence of the evolutions of this class of algorithms to the average of initial states. Moreover, for a random sequence of graphs generated using a time-varying B-irreducible sequence of probability matrices, we establish convergence rates for the proposed push-sum algorithm.
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