菱形网络链上的最快分布式共识平均问题
Fastest Distributed Consensus Averaging Problem on Chain of Rhombus Networks
摘要：
分布式共识已出现作为一个最重要的和主要的问题，在分布式计算的背景下，它已经收到了新的兴趣在传感器网络领域（由于在无线通信的最新进展），其中解决最快的分布式共识平均问题在不同的拓扑结构的网络是在这个问题的主要问题之一。本文给出了菱形网络链上最快分布式共识平均算法的解析解，其求解过程包括网络关联连通图的分层和半定规划，特别是松弛条件的求解，其中最优权值由松弛条件引发的特征多项式的归纳比较得到.归纳确定了包含SLEM的权矩阵特征值对应的特征多项式及其根。此外，为了说明菱形图的重要性，指出用菱形子图代替路网络中的单个节点，可以提高路网络的收敛速度。
英文摘要：
Distributed consensus has appeared as one of the most important and primary problems in the context of distributed computation and it has received renewed interest in the field of sensor networks (due to recent advances in wireless communications), where solving fastest distributed consensus averaging problem over networks with different topologies is one of the primary problems in this issue. Here in this work analytical solution for the problem of fastest distributed consensus averaging algorithm over Chain of Rhombus networks is provided, where the solution procedure consists of stratification of associated connectivity graph of the network and semidefinite programming, particularly solving the slackness conditions, where the optimal weights are obtained by inductive comparing of the characteristic polynomials initiated by slackness conditions. Also characteristic polynomial together with its roots corresponding to eigenvalues of weight matrix including SLEM of network is determined inductively. Moreover to see the importance of rhombus graphs it is indicated that convergence rate of path network increases by replacing a single node by a rhombus sub graph within the path network.
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。
