Subgraph Matching via Partial Optimal Transport

TL;DR

This paper introduces a novel subgraph matching method using partial fused Gromov-Wasserstein distance, demonstrating improved efficiency, robustness to noise, and faster query times on synthetic and real datasets.

Contribution

It formulates subgraph matching as a partial fused Gromov-Wasserstein problem and develops an efficient sliding approach for large graphs.

Findings

Outperforms state-of-the-art methods on synthetic datasets

Exhibits robustness to noise in datasets

Achieves very fast query times

Abstract

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.