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Distributed Averaging Using Periodic Gossiping

机译：使用定期八卦进行分布式平均

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摘要

The distributed averaging problem is a consensus problem whose objective is to devise a protocol which will enable all the members of a group of autonomous agents to compute the average of the initial values of their individual consensus variables in a distributed manner. Periodic gossiping is a deterministic method for solving the distributed averaging problem by stipulating that each pair of agents which are allowed to gossip, do so repeatedly in accordance with a prespecified periodic schedule. Agent pairs which are allowed to gossip correspond to edges on a given connected, undirected graph. In general, the rate at which the agents' consensus variables converge to the desired average value depends on the order in which the gossips occur over a period. The main contributions of this paper are first to characterize the classes of periodic gossip sequences which have the same convergence rate and second to prove that if the graph of allowable gossips is a tree with each edge restricted to gossiping once per period, the convergence rate is quite surprisingly, fixed and invariant over all possible periodic gossip sequences the graph allows. To arrive at these results, a new and unusual graph theoretic concept, namely the transfer function of a node of an undirected graph, is used. Among all the trees with the same number of edges, optimal tree structures, which yield the fastest convergence rate, can then be sought.
机译：分布式平均问题是一个共识问题，其目的是设计一种协议，该协议将使一组自治代理的所有成员能够以分布式方式计算其各个共识变量初始值的平均值。定期八卦是一种确定性方法，它通过规定允许被允许进行八卦的每一对代理按照预定的定期时间表重复进行来解决分布式平均问题。允许闲聊的代理对对应于给定连接的，无向图上的边。通常，代理商的共识变量收敛到所需平均值的速率取决于闲话在一段时间内发生的顺序。本文的主要贡献是首先描述具有相同收敛速率的周期性八卦序列的类别，其次证明如果允许的八卦图是一棵树，每个边每个周期仅限于八卦一次，则收敛速率为非常令人惊讶的是，该图允许的所有可能的周期性八卦序列都是固定不变的。为了获得这些结果，使用了一种新的不寻常的图论概念，即无向图的节点的传递函数。然后，在具有相同边数的所有树中，可以寻找产生最快收敛速度​​的最佳树结构。

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