Survivors in Leader Election Algorithms

Ravi Kalpathy, H. Mahmoud, W. Rosenkrantz
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引用次数: 8

Abstract

We consider the number of survivors in a broad class of fair leader election algorithms after a number of election rounds. We give sufficient conditions for the number of survivors to converge to a product of independent identically distributed random variables. The number of terms in the product is determined by the round number considered. Each individual term in the product is a limit of a scaled random variable associated with the splitting protocol. The proof is established via convergence (to 0) of the first-order Wasserstein distance from the product limit. In a broader context, the paper is a case study of a class of stochastic recursive equations. We give two illustrative examples, one with binomial splitting protocol (for which we show that a normalized version is asymptotically Gaussian) and one with uniform splitting protocol.
领袖选举算法中的幸存者
我们考虑在一系列选举轮之后,在广泛的公平领导人选举算法中幸存的人数。给出了幸存者数量收敛于独立同分布随机变量的乘积的充分条件。产品中的项数由所考虑的整数决定。乘积中的每个单独项都是与拆分协议相关的缩放随机变量的极限。证明是通过从乘积极限的一阶Wasserstein距离的收敛(到0)建立的。在更广泛的背景下,本文是一类随机递归方程的案例研究。我们给出了两个说明性的例子,一个是二项分裂协议(我们证明了一个归一化版本是渐近高斯的),一个是均匀分裂协议。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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