论文标题
通过离散时混合动力学定理分布式算法的设计方法
A Design Method of Distributed Algorithms via Discrete-time Blended Dynamics Theorem
论文作者
论文摘要
我们开发了使用分布式计算算法的混合动力学定理的离散时间版本。混合动力学定理可以预测异质多机构系统的行为。因此，一旦我们获得了特定计算任务的混合动力学，就可以轻松地发生针对单个异质剂的节点动力学的设计思想。在连续的时间情况下，通过相邻代理之间的高耦合增益来实现混合动力学的预测。在离散时间的情况下，我们提出了同等的动作，我们在本文中称之为多步耦合。与连续的时间情况相比，混合动力学可以根据耦合矩阵具有更多的变化。通过三个申请证明了这一好处；网络大小的分布式估计，PageRank的分布式计算以及图形的度序列的分布式计算，该计算分别与双重性，柱状，柱状和行相结合的矩阵对应于耦合。
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.
