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

A single integer quadratic program for the graph edit distance and graph matching problems.

Authors : Romain Raveaux

Personal Website : http://romain.raveaux.free.fr/

Organisation : Université François Rabelais de Tours, Laboratoire d’Informatique Fondamentale et Appliquée (EA 6300), 64 avenue Jean Portalis, Tours, France

The paper : The paper is published in Pattern Recognition Letters (https://doi.org/10.1016/j.patrec.2021.02.014) and a pre-print version can be found here (https://hal.archives-ouvertes.fr/hal-03163084)

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.

Keywords : Graph edit distance, graph matching, discrete optimization

Content of the website :

1. Theoretical justification

2. Some detailed examples

3. Source code

4. Data base and cost functions

5. Benchmark and Results

Graphical Abstract :