The NP-hardness of the Gromov-Wasserstein distance
Abstract
This note addresses the property frequently mentioned in the literature that the Gromov-Wasserstein (GW) distance is NP-hard. We provide the details on the non-convex nature of the GW optimization problem that imply NP-hardness of the GW distance between finite spaces for any instance of an input data. We further illustrate the non-convexity of the problem with several explicit examples.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.06525
- arXiv:
- arXiv:2408.06525
- Bibcode:
- 2024arXiv240806525K
- Keywords:
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- Statistics - Machine Learning;
- Computer Science - Machine Learning