This paper addresses the problem of multiple graph matching (MGM) by considering both offline batch mode and online setting. We explore the concept of cycle-consistency over pairwise matchings and formulate the problem as finding optimal composition path on the supergraph, whose vertices refer to graphs and edge weights denote score function regarding consistency and affinity. By our theoretical study we show that the offline and online MGM on supergraph can be converted to finding all pairwise shortest paths and single-source shortest paths respectively. We adopt the Floyd algorithm [1] and shortest path faster algorithm (SPFA) [2] , [3] to effectively find the optimal path. Extensive experimental results show our methods surpass state-of-the-art MGM methods, including CAO [4] , MISM [5] , IMGM [6] , and many other recent methods in offline and online settings. Source code will be made publicly available.

中文翻译：

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通过在 Supergraph 上寻找最短路径来统一离线和在线多图匹配

本文通过考虑离线批处理模式和在线设置来解决多图匹配（MGM）问题。我们探索了成对匹配上的循环一致性的概念，并将问题表述为在超图上寻找最佳组合路径，其顶点指的是图，边权重表示关于一致性和亲和力的得分函数。通过我们的理论研究，我们表明超图上的离线和在线 MGM 可以转换为分别找到所有成对最短路径和单源最短路径。我们采用 Floyd 算法[1] 和最短路径更快算法（SPFA） [2] , [3]有效地找到最优路径。广泛的实验结果表明我们的方法超越了最先进的 MGM 方法，包括 CAO[4] , 管理信息系统 [5] , IMGM [6]，以及离线和在线设置中的许多其他最新方法。源代码将公开提供。