Subgraph Matching via Partial Optimal Transport

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 real-world datasets. In particular, our methods exhibit robustness with respect to noise in the datasets and achieve very fast query times.