In this work, we propose a novel approach for subgraph matching, the problem of finding a given query graph in a large source graph, based on the fused Gromov-Wasserstein distance. We formulate the subgraph matching problem as a partial fused Gromov-Wasserstein problem, which allows us to build on existing theory and computational methods in order to solve this challenging problem. We extend our method by employing a subgraph sliding approach, which makes it efficient even for large graphs. In numerical experiments, we showcase that our new algorithms have the ability to outperform state-of-the-art methods for subgraph matching on synthetic as well as realworld datasets. In particular, our methods exhibit robustness with respect to noise in the datasets and achieve very fast query times.

翻译：在本研究中，我们提出了一种基于融合Gromov-Wasserstein距离的子图匹配新方法，该问题旨在大型源图中查找给定查询图。我们将子图匹配问题构建为部分融合Gromov-Wasserstein问题，从而能够基于现有理论和计算方法来解决这一挑战性问题。通过采用子图滑动策略扩展了我们的方法，使其即使对于大型图也能高效运行。在数值实验中，我们证明新算法在合成数据集和真实数据集上的子图匹配性能均能超越现有最优方法。特别值得注意的是，我们的方法对数据集噪声具有鲁棒性，并能实现极快的查询速度。