Note on computational complexity of the Gromov-Wasserstein distance
Machine Learning
2026-02-10 v4 Machine Learning
Abstract
This note addresses computational difficulty of the Gromov-Wasserstein distance frequently mentioned in the literature. We provide details on the structure of the Gromov-Wasserstein distance optimization problem that show its non-convex quadratic nature for any instance of an input data. We further illustrate the non-convexity of the problem with several explicit examples.
Cite
@article{arxiv.2408.06525,
title = {Note on computational complexity of the Gromov-Wasserstein distance},
author = {Natalia Kravtsova},
journal= {arXiv preprint arXiv:2408.06525},
year = {2026}
}
Comments
This is an updated version of the note previously titled "The NP-hardness of the Gromov-Wasserstein distance." This version corrects deficiencies in the previous version