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An Upper Bound on the Convergence Time for Quantized Consensus of Arbitrary Static Graphs

机译：任意静态图量化共识的收敛时间的上界

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摘要

We analyze a class of distributed quantized consensus algorithms for arbitrary static networks. In the initial setting, each node in the network has an integer value. Nodes exchange their current estimate of the mean value in the network, and then update their estimation by communicating with their neighbors in a limited capacity channel in an asynchronous clock setting. Eventually, all nodes reach consensus with quantized precision. We analyze the expected convergence time for the general quantized consensus algorithm proposed by Kashyap (“Quantized consensus,” , 2007). We use the theory of electric networks, random walks, and couplings of Markov chains to derive an upper bound for the expected convergence time on an arbitrary graph of size , improving on the state of art bound of for quantized consensus algorithms. Our result is not dependent on graph topology. Example of complete graphs is given to show how to extend the analysis to graphs of given topology. This is consistent with the analysis in “Convergence speed of binary interval consensus,” (M. Draief and M. Vojnovic, , 2012.
机译：我们分析了用于任意静态网络的一类分布式量化共识算法。在初始设置中，网络中的每个节点都有一个整数值。节点交换它们在网络中当前的平均值估计值，然后通过在异步时钟设置中在有限容量的信道中与邻居通信来更新其估计值。最终，所有节点都以量化精度达成共识。我们分析了Kashyap提出的通用量化共识算法的预期收敛时间（“量化共识”，2007年）。我们使用网络，随机游走和马尔可夫链的耦合理论在任意大小的图上得出预期收敛时间的上限，从而改进了量化共识算法的现有技术水平。我们的结果不依赖于图拓扑。给出了完整图形的示例，以显示如何将分析扩展到给定拓扑的图形。这与“二进制区间共识的收敛速度”中的分析一致（M. Draief和M. Vojnovic，2012年。

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