通用星型和K核星型网络最快分布式共识问题的一种解决方案
A Solution to Fastest Distributed Consensus Problem for Generic Star & K-cored Star Networks
摘要：
分布式平均一致性是分散计算算法中的主要机制。在分布式平均共识算法中，每个节点都有一个初始状态，目标是计算每个节点的初始状态的平均值。为了完成这一任务，每个节点通过使用相邻节点之间的本地通信，通过其自身和邻居的状态的加权平均来更新其状态。在拓扑结构固定的网络中，分布式平均共识算法的收敛速度取决于权值的选择。研究了分布式平均共识算法中的权值优化问题。这里考虑的网络拓扑是一个星形网络，其中分支具有不同的长度。根据网络的拓扑参数，给出了最优权值和算法收敛速度的闭式公式。此外，一般的K-核心星形拓扑结构已被引入作为一种替代的星形拓扑结构。与星型拓扑相比，引入的拓扑具有更快的收敛速度。仿真结果表明，与其他常用的加权方法相比，最优加权方法具有更好的性能。
英文摘要：
Distributed average consensus is the main mechanism in algorithms for decentralized computation. In distributed average consensus algorithm each node has an initial state, and the goal is to compute the average of these initial states in every node. To accomplish this task, each node updates its state by a weighted average of its own and neighbors' states, by using local communication between neighboring nodes. In the networks with fixed topology, convergence rate of distributed average consensus algorithm depends on the choice of weights. This paper studies the weight optimization problem in distributed average consensus algorithm. The network topology considered here is a star network where the branches have different lengths. Closed-form formulas of optimal weights and convergence rate of algorithm are determined in terms of the network's topological parameters. Furthermore generic K-cored star topology has been introduced as an alternative to star topology. The introduced topology benefits from faster convergence rate compared to star topology. By simulation better performance of optimal weights compared to other common weighting methods has been proved.
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