论文标题
多代理网络中图形匹配的分布式计算
Distributed Computation of Graph Matching in Multi-Agent Networks
论文作者
论文摘要
这项工作考虑了多代理网络，考虑了两个无向图和连接图之间的一对一顶点对应关系的分布式计算，这称为\ textit {Graph {Graph Matching}。给定两个\ textit {isomorphic}和\ textit {inmymmetric}图，有一个唯一的排列矩阵，将一个图中的顶点映射到另一个图的顶点。基于Aflalo等人中图匹配的凸松弛。 （2015年），我们建议使用相互作用图连接的多个代理的网络，将图形匹配作为作为平等约束和全局设置约束的分布式凸优化问题的分布式计算。网络中的每个代理只知道这两个图的每个邻接矩阵的一列，并且所有代理都通过与邻居交换信息来协作学习图形匹配。所提出的算法采用预测的原始双梯度方法来处理平等约束和设定约束。在提出的算法下，对置换矩阵的试剂的估计值在全球和指数上呈最佳置换。最后，给出仿真结果以说明该方法的有效性。
This work considers the distributed computation of the one-to-one vertex correspondences between two undirected and connected graphs, which is called \textit{graph matching}, over multi-agent networks. Given two \textit{isomorphic} and \textit{asymmetric} graphs, there is a unique permutation matrix that maps the vertices in one graph to the vertices in the other. Based on a convex relaxation of graph matching in Aflalo et al. (2015), we propose a distributed computation of graph matching as a distributed convex optimization problem subject to equality constraints and a global set constraint, using a network of multiple agents whose interaction graph is connected. Each agent in the network only knows one column of each of the adjacency matrices of the two graphs, and all agents collaboratively learn the graph matching by exchanging information with their neighbors. The proposed algorithm employs a projected primal-dual gradient method to handle equality constraints and a set constraint. Under the proposed algorithm, the agents' estimates of the permutation matrix converge to the optimal permutation globally and exponentially fast. Finally, simulation results are given to illustrate the effectiveness of the method.
