Note on computational complexity of the Gromov-Wasserstein distance

arXiv:2408.06525v4 Announce Type: replace
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.