On the unification of the graph edit distance and graph matching problems

TL;DR

This paper unifies the graph edit distance and graph matching problems into a single model, enabling the use of existing solvers across both problems by proving their equivalence under reformulated error models.

Contribution

It introduces a unified framework for graph edit distance and graph matching, bridging two previously separate research areas.

Findings

Proves the equivalence of GED and graph matching under reformulated error models.

Enables cross-application of solvers from both problem domains.

Facilitates unified approaches to error-tolerant graph matching.

Abstract

Error-tolerant graph matching gathers an important family of problems. These problems aim at finding correspondences between two graphs while integrating an error model. In the Graph Edit Distance (GED) problem, the insertion/deletion of edges/nodes from one graph to another is explicitly expressed by the error model. At the opposite, the problem commonly referred to as "graph matching" does not explicitly express such operations. For decades, these two problems have split the research community in two separated parts. It resulted in the design of different solvers for the two problems. In this paper, we propose a unification of both problems thanks to a single model. We give the proof that the two problems are equivalent under a reformulation of the error models. This unification makes possible the use on both problems of existing solving methods from the two communities.