Enhanced Phase Clocks, Population Protocols, and Fast Space Optimal Leader Election

L. Gąsieniec, Grzegorz Stachowiak
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引用次数: 14

Abstract

The model of population protocols refers to the growing in popularity theoretical framework suitable for studying pairwise interactions within a large collection of simple indistinguishable entities, frequently called agents. In this article, the emphasis is on the space complexity of fast leader election in population protocols governed by the random scheduler, which uniformly at random selects pairwise interactions between n agents. One of the main results of this article is the first fast space optimal leader election protocol, which works with high probability. The new protocol operates in parallel time O(log2 n) equivalent to O(nlog2 n) sequential pairwise interactions with each agent’s memory space limited to O(log log n) states. This double logarithmic space utilisation matches asymptotically the lower bound ½log log n on the number of states utilised by agents in any leader election algorithm with the running time o(n\polylog n); see Reference [7]. Our new solution expands also on the classical concept of phase clocks used to synchronise and to coordinate computations in distributed algorithms. In particular, we formalise the concept and provide a rigorous analysis of phase clocks operating in nested modes. Our arguments are also valid for phase clocks propelled by multiple leaders. The combination of the two results in the first time-space efficient leader election algorithm. We also provide a complete formal argumentation, indicating that our solution is always correct, fast, and it works with high probability.
增强相位时钟,人口协议和快速空间最优领导者选举
群体协议模型是指一种日益流行的理论框架,适用于研究大量简单的不可区分实体(通常称为代理)内的成对相互作用。在本文中,重点研究了由随机调度程序控制的群体协议中快速领导者选择的空间复杂性,随机调度程序均匀地随机选择n个代理之间的两两交互。本文的主要成果之一是第一个快速空间最优领导者选举协议,该协议具有高概率。新协议以并行时间O(log2n)运行,相当于O(nlog2n)个顺序成对交互,每个代理的内存空间限制为O(log log n)个状态。这种双对数空间利用率渐近匹配运行时间为o(n\polylog n)的任何领导者选举算法中代理使用的状态数的下界½log log n;参见文献[7]。我们的新解决方案还扩展了用于同步和协调分布式算法计算的相位时钟的经典概念。特别是,我们形式化了这个概念,并提供了在嵌套模式下运行的相位时钟的严格分析。我们的论点也适用于由多个领导者推动的相位时钟。两者结合得到了第一个时空高效的领导人选举算法。我们还提供了一个完整的形式论证,表明我们的解决方案始终是正确的,快速的,并且具有高概率。
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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