两星型网络融合的最快分布式共识问题
Fastest Distributed Consensus Problem on Fusion of Two Star Networks
摘要：
在不同拓扑结构的网络上寻找最快分布式共识问题的最优权值已经是一个活跃的研究领域。在这项工作中，我们提出了一个最快的分布式共识的问题的分析解决方案的网络融合形成的两个不同的对称星型网络，或者换句话说，网络由两个不同的对称星型网络共享同一个中心节点。求解过程包括网络关联连通图的分层和半定规划（SDP），特别是松弛条件的求解，其中最优权值通过松弛条件引发的特征多项式的归纳比较得到。一些数值模拟进行了调查之间的权衡两个融合星型网络的参数，即分支的长度和数量。
英文摘要：
Finding optimal weights for the problem of Fastest Distributed Consensus on networks with different topologies has been an active area of research for a number of years. Here in this work we present an analytical solution for the problem of Fastest Distributed Consensus for a network formed from fusion of two different symmetric star networks or in other words a network consists of two different symmetric star networks which share the same central node. The solution procedure consists of stratification of associated connectivity graph of network and Semidefinite Programming (SDP), particularly solving the slackness conditions, where the optimal weights are obtained by inductive comparing of the characteristic polynomials initiated by slackness conditions. Some numerical simulations are carried out to investigate the trade-off between the parameters of two fused star networks, namely the length and number of branches.
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