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arXiv 2210.05142eess.SYcs.SY
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基于离散时间混合动力学定理的分布式算法设计方法

A Design Method of Distributed Algorithms via Discrete-time Blended Dynamics Theorem

Jeong Woo Kim, Jin Gyu Lee, Donggil Lee, Hyungbo Shim

AI总结:

本文提出离散时间混合动力学定理,通过多步耦合机制设计异构多智能体分布式算法,并展示了其在网络规模估计、PageRank 计算和图度序列计算中的应用。

摘要:

我们提出了混合动力学定理的离散时间版本,用于设计分布式计算算法。混合动力学定理能够预测异构多智能体系统的行为。因此,一旦我们为特定的计算任务得到混合动力学,针对单个异构智能体的节点动力学设计思路就很容易产生。在连续时间情形下,混合动力学的预测能力依赖于相邻智能体之间的高耦合增益。在离散时间情形下,我们提出了一种等效机制,本文称之为多步耦合。与连续时间情形相比,混合动力学可以根据耦合矩阵的不同而具有更丰富的形式。这一优势通过三个应用加以展示:网络规模的分布式估计、PageRank 的分布式计算以及图的度序列的分布式计算,它们分别对应于双随机矩阵、列随机矩阵和行随机矩阵的耦合。

英文摘要:

We develop a discrete-time version of the blended dynamics theorem for the use of designing distributed computation algorithms. The blended dynamics theorem enables to predict the behavior of heterogeneous multi-agent systems. Therefore, once we get a blended dynamics for a particular computational task, design idea of node dynamics for individual heterogeneous agents can easily occur. In the continuous-time case, prediction by blended dynamics was enabled by high coupling gain among neighboring agents. In the discrete-time case, we propose an equivalent action, which we call multi-step coupling in this paper. Compared to the continuous-time case, the blended dynamics can have more variety depending on the coupling matrix. This benefit is demonstrated with three applications; distributed estimation of network size, distributed computation of the PageRank, and distributed computation of the degree sequence of a graph, which correspond to the coupling by doubly-stochastic, column-stochastic, and row-stochastic matrices, respectively.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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