[16] Richard Mansfield Dudley. The speed of mean glivenko-cantelli convergence. The Annals of Mathematical Statistics, 40(1):40-50, 1969.
[17] RM Dudley. Real analysis and probability, 2002.
[18] Nghia Duong-Trung, Minh-Hoang Nguyen, and Hanh TH Nguyen. Clustering stability via concept-based nonnegative matrix factorization. In Proceedings of the 3rd International Conference on Machine Learning and Soft Computing, pages 49-54, 2019.
[19] Nicolas Fournier and Arnaud Guillin. On the rate of convergence in Wasserstein distance of the empirical measure. *Probability theory and related fields*, 162(3-4):707-738, 2015.
[20] Kyle Fox and Jiashuai Lu. A near-linear time approximation scheme for geometric transportation with arbitrary supplies and spread. In Proc. 36th Annual Symposium on Computational Geometry, pages 45:1-45:18, 2020.
[21] H. N. Gabow and R.E. Tarjan. Faster scaling algorithms for network problems. SIAM J. Comput., 18:1013-1036, October 1989. ISSN 0097-5397.
[22] Harold N. Gabow and Robert Endre Tarjan. Faster scaling algorithms for general graph-matching problems. J. ACM, 38(4):815-853, 1991.
[23] Javier González-Delgado, Alberto González-Sanz, Juan Cortés, and Pierre Neuvial. Two-sample goodness-of-fit tests on the flat torus based on Wasserstein distance and their relevance to structural biology. arXiv preprint arXiv:2108.00165, 2021.
[24] Xin Guo, Johnny Hong, Tianyi Lin, and Nan Yang. Relaxed wasserstein with applications to gans. In ICASSP 2021-2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 3325-3329. IEEE, 2021.
[25] Masaaki Imaizumi, Hirofumi Ota, and Takuo Hamaguchi. Hypothesis test and confidence analysis with Wasserstein distance on general dimension. Neural Computation, 34(6):1448-1487, 2022.
[26] Andrey Boris Khesin, Aleksandar Nikolov, and Dmitry Paramonov. Preconditioning for the geometric transportation problem. arXiv preprint arXiv:1902.08384, 2019.
[27] Soheil Kolouri, Navid Naderializadeh, Gustavo K Rohde, and Heiko Hoffmann. Wasserstein embedding for graph learning. arXiv preprint arXiv:2006.09430, 2020.
[28] Harold W Kuhn. The hungarian method for the assignment problem. Naval research logistics quarterly, 2(1-2):83-97, 1955.
[29] Nathaniel Lahn and Sharath Raghevendra. An  $o(n^{5/4})$  time  $\varepsilon$ -approximation algorithm for rms matching in a plane. In Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 869-888. SIAM, 2021.
[30] Nathaniel Lahn, Sharath Raghvendra, and Kaiyi Zhang. A push-relabel based additive approximation for optimal transport. arXiv preprint arXiv:2203.03732, 2022.
[31] Tilman Lange, Volker Roth, Mikio L Braun, and Joachim M Buhmann. Stability-based validation of clustering solutions. Neural computation, 16(6):1299-1323, 2004.
[32] Richard J Lipton and Robert Endre Tarjan. Applications of a planar separator theorem. SIAM journal on computing, 9(3):615-627, 1980.
[33] Huidong Liu, GU Xianfeng, and Dimitris Samaras. A two-step computation of the exact gan wasserstein distance. In International Conference on Machine Learning, pages 3159-3168. PMLR, 2018.
[34] Huidong Liu, Xianfeng Gu, and Dimitris Samaras. Wasserstein gan with quadratic transport cost. In Proceedings of the IEEE/CVF international conference on computer vision, pages 4832-4841, 2019.