完备n叉树网络上的最快分布式共识平均问题
Fastest Distributed Consensus Averaging Problem on Perfect and Complete n-ary Tree networks
摘要：
解决最快的分布式共识平均问题（即，在具有不同拓扑结构的网络上找到边上的权重以最小化权重矩阵的第二大特征值模）是传感器网络领域中的主要研究领域之一，并且在这个问题中众所周知的网络之一是树形网络。在这项工作中，我们提出了最快的分布式共识平均算法的分层和半定规划的方法，为两种特殊类型的树网络，即完美和完整的n元树网络的问题的解析解。该方法基于最快分布式共识平均问题的凸性，通过对松弛条件下的特征多项式进行归纳比较，找到最优权值。此外，某些类型的分支（例如完美和完整的n元树分支）的边的最佳权重独立于网络的其余部分来确定。
英文摘要：
Solving fastest distributed consensus averaging problem (i.e., finding weights on the edges to minimize the second-largest eigenvalue modulus of the weight matrix) over networks with different topologies is one of the primary areas of research in the field of sensor networks and one of the well known networks in this issue is tree network. Here in this work we present analytical solution for the problem of fastest distributed consensus averaging algorithm by means of stratification and semidefinite programming, for two particular types of tree networks, namely perfect and complete n-ary tree networks. Our method in this paper is based on convexity of fastest distributed consensus averaging problem, and inductive comparing of the characteristic polynomials initiated by slackness conditions in order to find the optimal weights. Also the optimal weights for the edges of certain types of branches such as perfect and complete n-ary tree branches are determined independently of rest of the network.
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