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This note addresses computational difficulty of the Gromov-Wasserstein distance frequently mentioned in the literature.
Assignment problems and the location of economic activities
Tjalling C. Koopmans and Martin Beckmann · 1957
Earlier work this paper cites.
On the use of exact and heuristic cutting plane methods for the quadratic assignment problem
Mokhtar S. Bazaraa and Hanif D. Sherali · 1982
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The principal minor test for semidefinite matrices
John E. Prussing · 1986
Earlier work this paper cites.
Polynomial time algorithms for some classes of constrained nonconvex quadratic problems
Panos M Pardalos · 1990
Earlier work this paper cites.
Quadratic programming with one negative eigenvalue is NP-hard
Panos M. Pardalos and Stephen A. Vavasis · 1991
Earlier work this paper cites.
Algorithms for the solution of quadratic knapsack problems
Panos M Pardalos, Yinyu Ye, and Chi-Geun Han · 1991
Earlier work this paper cites.
Nonlinear programming, 1999
Dimitri P. Bertsekas · 1999
Earlier work this paper cites.
Limit cycles for the competitive three dimensional Lotka–Volterra system
Dongmei Xiao and Wenxia Li · 2000
Earlier work this paper cites.
On the use of Gromov–Hausdorff distances for shape comparison
Facundo Mémoli · 2007
Earlier work this paper cites.
Complexity Theory: Quadratic Programming
Stephen A. Vavasis · 2009
Earlier work this paper cites.
Gromov–Wasserstein distances and the metric approach to object matching
Facundo Mémoli · 2011
Earlier work this paper cites.
Gromov–Wasserstein averaging of kernel and distance matrices
Gabriel Peyré, Marco Cuturi, and Justin Solomon · 2016
Earlier work this paper cites.
Learning generative models across incomparable spaces
Charlotte Bunne, David Alvarez-Melis, Andreas Krause, and Stefanie Jegelka · 2019
Cited alongside, same era.
The Gromov–Wasserstein distance between networks and stable network invariants
Samir Chowdhury and Facundo Mémoli · 2019
Cited alongside, same era.
Computational optimal transport: With applications to data science
Gabriel Peyré and Marco Cuturi · 2019
Cited alongside, same era.
Scalable Gromov–Wasserstein learning for graph partitioning and matching
Hongteng Xu, Dixin Luo, and Lawrence Carin · 2019
Cited alongside, same era.
Inferring spatial and signaling relationships between cells from single cell transcriptomic data
Zixuan Cang and Qing Nie · 2020
Cited alongside, same era.
Partial optimal tranport with applications on positive-unlabeled learning
Laetitia Chapel, Mokhtar Z Alaya, and Gilles Gasso · 2020
Gromov–Wasserstein distances between Gaussian distributions
Julie Delon, Agnes Desolneux, and Antoine Salmona · 2022
Later among the works it cites.
SCOT: single-cell multi-omics alignment with optimal transport
Pinar Demetci, Rebecca Santorella, Björn Sandstede, William Stafford Noble, and Ritambhara Singh · 2022
Later among the works it cites.
Cross-domain imitation learning via optimal transport
Arnaud Fickinger, Samuel Cohen, Stuart Russell, and Brandon Amos · 2022
Later among the works it cites.
Linear-time Gromov–Wasserstein distances using low rank couplings and costs
Meyer Scetbon, Gabriel Peyré, and Marco Cuturi · 2022
Later among the works it cites.
Representing graphs via Gromov–Wasserstein factorization
Hongteng Xu, Jiachang Liu, Dixin Luo, and Lawrence Carin · 2022
Later among the works it cites.
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Cited alongside, same era.
Graph optimal transport for cross-domain alignment
Liqun Chen, Zhe Gan, Yu Cheng, Linjie Li, Lawrence Carin, and Jingjing Liu · 2020
Cited alongside, same era.
Fused Gromov–Wasserstein distance for structured objects
Titouan Vayer, Laetitia Chapel, Rémi Flamary, Romain Tavenard, and Nicolas Courty · 2020
Cited alongside, same era.
Generalized spectral clustering via Gromov–Wasserstein learning
Samir Chowdhury and Tom Needham · 2021
Cited alongside, same era.
POT: Python Optimal Transport
Rémi Flamary, Nicolas Courty, Alexandre Gramfort, Mokhtar Z. Alaya, Aurélie Boisbunon, Stanislas Chambon, Laetitia Chapel, Adrien Corenflos, Kilian Fatras, Nemo Fournier, Léo Gautheron, Nathalie T.H. Gayraud, Hicham Janati, Alain Rakotomamonjy, Ievgen Redko, Antoine Rolet, Antony Schutz, Vivien Seguy, Danica J. Sutherland, Romain Tavenard, Alexander Tong, and Titouan Vayer · 2021
Cited alongside, same era.
Flow-based alignment approaches for probability measures in different spaces
Tam Le, Nhat Ho, and Makoto Yamada · 2021
Cited alongside, same era.
Optimal Transport Tools (OTT): A JAX toolbox for all things Wasserstein
Marco Cuturi, Laetitia Meng-Papaxanthos, Yingtao Tian, Charlotte Bunne, Geoff Davis, and Olivier Teboul · 2022
Cited alongside, same era.
Shreya Arya, Arnab Auddy, Ranthony Edmonds, Sunhyuk Lim, Facundo Memoli, and Daniel Packer · 2023
Later among the works it cites.
Semidefinite relaxations of the Gromov–Wasserstein distance
Junyu Chen, Binh T Nguyen, and Yong Sheng Soh · 2023
Later among the works it cites.
Scalable Gromov–Wasserstein based comparison of biological time series
Natalia Kravtsova, Reginald L. McGee II, and Adriana T. Dawes · 2023
Later among the works it cites.
The ultrametric Gromov–Wasserstein distance
Facundo Mémoli, Axel Munk, Zhengchao Wan, and Christoph Weitkamp · 2023
Later among the works it cites.
Aryan Tajmir Riahi, Chenwei Zhang, James Chen, Anne Condon, and Khanh Dao Duc · 2023
Later among the works it cites.
Entropic Gromov–Wasserstein distances: Stability and algorithms
Gabriel Rioux, Ziv Goldfeld, and Kengo Kato · 2023
Later among the works it cites.
Efficient solvers for partial Gromov–Wasserstein
Yikun Bai, Rocio Diaz Martin, Hengrong Du, Ashkan Shahbazi, and Soheil Kolouri · 2024
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