Convergence Speed in Distributed Consensus and Control
<|reference_start|>Convergence Speed in Distributed Consensus and Control: 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.<|reference_end|>
@article{olshevsky2006convergence,
    title={Convergence Speed in Distributed Consensus and Control},
    author={Alex Olshevsky, John N. Tsitsiklis},
    journal={arXiv preprint arXiv:math/0612682},
    year={2006},
    archivePrefix={arXiv},
    eprint={math/0612682},
    primaryClass={math.OC cs.SY}
}