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Inspired by the matching of supply to demand in logistical problems, the optimal transport (or Monge--Kantorovich) problem involves the matching of probability distributions defined over a geometric domain such as a surface or manifold.
Frank L Hitchcock, The distribution of a product from several sources to numerous localities , Studies in Applied Mathematics 20
1941
Earlier work this paper cites.
Tjalling C Koopmans, Exchange ratios between cargoes on various routes , (1941)
1941
Earlier work this paper cites.
Leonid Vitalievich Kantorovich, On the translocation of masses , Dokl. Akad. Nauk SSSR, vol. 37, 1942, pp. 199–201
1942
Earlier work this paper cites.
Morton Slater, Lagrange multipliers revisited , Cowles Commission Discussion Paper (1950), no. 403, 1–13
1950
Earlier work this paper cites.
Solomon Kullback and Richard A Leibler, On information and sufficiency , The Annals of Mathematical Statistics 22
1951
Earlier work this paper cites.
Jim Douglas and Henry H Rachford, On the numerical solution of heat conduction problems in two and three space variables , Transactions of the American Mathematical Society 82
1956
Earlier work this paper cites.
Lester Randolph Ford Jr. and Delbert Ray Fulkerson, Solving the transportation problem , Management Science 3
1956
Earlier work this paper cites.
Morton Klein, A primal method for minimal cost flows with applications to the assignment and transportation problems , Management Science 14
1967
Earlier work this paper cites.
Richard Sinkhorn and Paul Knopp, Concerning nonnegative matrices and doubly stochastic matrices , Pacific Journal of Mathematics 21
1967
Earlier work this paper cites.
Sathamangalam R.S̃rinivasa Varadhan, On the behavior of the fundamental solution of the heat equation with variable coefficients , Communications on Pure and Applied Mathematics 20
1967
Earlier work this paper cites.
Hirofumi Uzawa, Iterative methods for concave programming , Studies in Linear and Non-Linear Programming 2
1968
Earlier work this paper cites.
Leonid Nisonovich Vaseršteĭn, Markov processes over denumerable products of spaces, describing large systems of automata , Problemy Peredachi Informatsii 5
1969
Earlier work this paper cites.
Roland L’vovich Dobrushin, Definition of random variables by conditional distributions , Teoriya Veroyatnostei i ee Primeneniya 15
1970
Earlier work this paper cites.
Jason Altschuler, Jonathan Weed, and Philippe Rigollet, Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration , Proc. NIPS, 2017, pp. 1961–1971
1971
Earlier work this paper cites.
Sartaj Sahni and Teofilo Gonzalez, P-complete approximation problems , Journal of the ACM (JACM) 23
1976
Earlier work this paper cites.
Pierre-Louis Lions and Bertrand Mercier, Splitting algorithms for the sum of two nonlinear operators , SIAM Journal on Numerical Analysis 16
1979
Earlier work this paper cites.
Adrian Bowyer, Computing Dirichlet tessellations , The Computer Journal 24
1981
Earlier work this paper cites.
David F Watson, Computing the n n -dimensional Delaunay tessellation with application to Voronoi polytopes , The Computer Journal 24
1981
Earlier work this paper cites.
Franz Aurenhammer, Power diagrams: properties, algorithms and applications , SIAM Journal on Computing 16
1987
Earlier work this paper cites.
Joseph SB Mitchell, David M Mount, and Christos H Papadimitriou, The discrete geodesic problem , SIAM Journal on Computing 16
1987
Earlier work this paper cites.
Vladimir I. Oliker, Near radially symmetric solutions of an inverse problem in geometric optics , Inverse Problems 3
1987
Earlier work this paper cites.
by same author, Voronoi diagrams—a survey of a fundamental geometric data structure , ACM Computing Surveys (CSUR) 23
1991
Earlier work this paper cites.
Yann Brenier, Polar factorization and monotone rearrangement of vector-valued functions , Communications on Pure and Applied Mathematics 44
1991
Earlier work this paper cites.
Franz Aurenhammer, Friedrich Hoffmann, and Boris Aronov, Minkowski-type theorems and least-squares partitioning , Proceedings of the Eighth Annual Symposium on Computational Geometry, ACM, 1992, pp. 350–357
1992
Earlier work this paper cites.
K. Ahuja Ravindra, Thomas L Magnanti, and James B. Orlin, Network flows: theory, algorithms, and applications , 1993
1993
Earlier work this paper cites.
Robert John McCann, A convexity theory for interacting gases and equilibrium crystals , Ph.D. thesis, Princeton University, 1994
1994
Earlier work this paper cites.
Xu-Jia Wang, On the design of a reflector antenna , Inverse problems 12
1996
Earlier work this paper cites.
Robert J McCann, A convexity principle for interacting gases , Advances in Mathematics 128
1997
Earlier work this paper cites.
James B Orlin, A polynomial time primal network simplex algorithm for minimum cost flows , Mathematical Programming 78
1997
Earlier work this paper cites.
Richard Jordan, David Kinderlehrer, and Felix Otto, The variational formulation of the Fokker–Planck equation , SIAM Journal on Mathematical Analysis 29
1998
Earlier work this paper cites.
Scott Cohen and Leonidas Guibas, The earth mover’s distance under transformation sets , Proc. ICCV, vol. 2, IEEE, 1999, pp. 1076–1083
1999
Earlier work this paper cites.
James A Sethian, Fast marching methods , SIAM review 41
1999
Earlier work this paper cites.
Jean-David Benamou and Yann Brenier, A computational fluid mechanics solution to the Monge–Kantorovich mass transfer problem , Numerische Mathematik 84
2000
Earlier work this paper cites.
Yossi Rubner, Carlo Tomasi, and Leonidas J Guibas, The earth mover’s distance as a metric for image retrieval , International journal of computer vision 40
2000
Earlier work this paper cites.
Elizaveta Levina and Peter Bickel, The earth mover’s distance is the Mallows distance: Some insights from statistics , Proc. ICCV, vol. 2, IEEE, 2001, pp. 251–256
2001
Earlier work this paper cites.
by same author, Polar factorization of maps on Riemannian manifolds , Geometric and Functional Analysis 11
2001
Earlier work this paper cites.
Felix Otto, The geometry of dissipative evolution equations: the porous medium equation , (2001)
2001
Earlier work this paper cites.
by same author, Extended Monge–Kantorovich theory , Lecture Notes in Mathematics (2003), 91–122
2003
Earlier work this paper cites.
Anil Nirmal Hirani, Discrete exterior calculus , Ph.D. thesis, California Institute of Technology, 2003
2003
Earlier work this paper cites.
Cédric Villani, Topics in optimal transportation , no. 58, American Mathematical Soc., 2003
2003
Cited alongside, same era.
Steven Haker, Lei Zhu, Allen Tannenbaum, and Sigurd Angenent, Optimal mass transport for registration and warping , International Journal of Computer Vision 60
2004
Cited alongside, same era.
Grégoire Loeper and Francesca Rapetti, Numerical solution of the Monge–Ampère equation by a Newton’s algorithm , Comptes Rendus Mathematique 340
2005
Cited alongside, same era.
Federico Bassetti, Antonella Bodini, and Eugenio Regazzini, On minimum Kantorovich distance estimators , Statistics & probability letters 76
2006
Cited alongside, same era.
Stacy Miller, The problem of redistricting: the use of centroidal Voronoi diagrams to build unbiased congressional districts , Senior project, Whitman College (2007)
2007
Jean-David Benamou, Guillaume Carlier, Marco Cuturi, Luca Nenna, and Gabriel Peyré, Iterative Bregman projections for regularized transportation problems , SIAM Journal on Scientific Computing 37
2015
Later among the works it cites.
Fernando de Goes, Corentin Wallez, Jin Huang, Dmitry Pavlov, and Mathieu Desbrun, Power particles: an incompressible fluid solver based on power diagrams , ACM Transactions on Graphics 34
2015
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Jonathan Korman and Robert McCann, Optimal transportation with capacity constraints , Transactions of the American Mathematical Society 367
2015
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Matt Kusner, Yu Sun, Nicholas Kolkin, and Kilian Weinberger, From word embeddings to document distances , International Conference on Machine Learning, 2015, pp. 957–966
2015
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Lukas Svec, Sam Burden, and Aaron Dilley, Applying Voronoi diagrams to the redistricting problem , The UMAP Journal 28
2007
Cited alongside, same era.
John Lott, Some geometric calculations on Wasserstein space , Communications in Mathematical Physics 277
2008
Cited alongside, same era.
Kaare Brandt Petersen and Michael Syskind Pedersen, The matrix cookbook , Technical University of Denmark 7
2008
Cited alongside, same era.
by same author, Optimal transport: old and new , vol. 338, Springer Science & Business Media, 2008
2008
Cited alongside, same era.
Facundo Mémoli, Spectral Gromov–Wasserstein distances for shape matching , Proc. ICCV Workshops, IEEE, 2009, pp. 256–263
2009
Cited alongside, same era.
Ofir Pele and Michael Werman, Fast and robust earth mover’s distances , Proc. ICCV, IEEE, 2009, pp. 460–467
2009
Cited alongside, same era.
Jean-David Benamou, Brittany D Froese, and Adam M Oberman, Two numerical methods for the elliptic Monge-Ampère equation , ESAIM: Mathematical Modelling and Numerical Analysis 44
2010
Cited alongside, same era.
2015
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Jean-Marie Mirebeau, Numerical resolution of Euler equations, through semi-discrete optimal transport , Journées Équations aux Dérivées Partielles (2015), 1–16
2015
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Lipeng Ning, Tryphon T Georgiou, and Allen Tannenbaum, On matrix-valued Monge–Kantorovich optimal mass transport , IEEE Transactions on Automatic Control 60
2015
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Brendan Pass, Multi-marginal optimal transport: theory and applications , ESAIM: Mathematical Modelling and Numerical Analysis 49
2015
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Gabriel Peyré, Entropic approximation of Wasserstein gradient flows , SIAM Journal on Imaging Sciences 8
2015
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Filippo Santambrogio, Optimal transport for applied mathematicians , Springer, 2015
2015
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Justin Solomon, Fernando De Goes, Gabriel Peyré, Marco Cuturi, Adrian Butscher, Andy Nguyen, Tao Du, and Leonidas Guibas, Convolutional Wasserstein distances: Efficient optimal transportation on geometric domains , ACM Transactions on Graphics (TOG) 34
2015
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Jean-David Benamou, Guillaume Carlier, and Maxime Laborde, An augmented Lagrangian approach to Wasserstein gradient flows and applications , ESAIM: Proceedings and Surveys 54
2016
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Nicolas Bonneel, Gabriel Peyré, and Marco Cuturi, Wasserstein barycentric coordinates: histogram regression using optimal transport , ACM Transactions on Graphics 35
2016
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Lénaïc Chizat, Gabriel Peyré, Bernhard Schmitzer, and François-Xavier Vialard, An interpolating distance between optimal transport and Fisher–Rao metrics , Foundations of Computational Mathematics (2016), 1–44
2016
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2016
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Quentin Mérigot and Jean-Marie Mirebeau, Minimal geodesics along volume-preserving maps, through semidiscrete optimal transport , SIAM Journal on Numerical Analysis 54
2016
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Grégoire Montavon, Klaus-Robert Müller, and Marco Cuturi, Wasserstein training of restricted Boltzmann machines , Advances in Neural Information Processing Systems, 2016, pp. 3718–3726
2016
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Gabriel Peyré, Marco Cuturi, and Justin Solomon, Gromov–Wasserstein averaging of kernel and distance matrices , International Conference on Machine Learning, 2016, pp. 2664–2672
2016
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Justin Solomon, Gabriel Peyré, Vladimir G Kim, and Suvrit Sra, Entropic metric alignment for correspondence problems , ACM Transactions on Graphics (TOG) 35
2016
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by same author, Continuous-flow graph transportation distances , arXiv:1603.06927 (2016)
2016
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Martin Arjovsky, Soumith Chintala, and Léon Bottou, Wasserstein generative adversarial networks , International Conference on Machine Learning, 2017, pp. 214–223
2017
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2017
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Yongxin Chen, Tryphon T Georgiou, and Allen Tannenbaum, Matrix optimal mass transport: a quantum mechanical approach , IEEE Transactions on Automatic Control (2017)
2017
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2017
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Nicolas Courty, Rémi Flamary, Devis Tuia, and Alain Rakotomamonjy, Optimal transport for domain adaptation , PAMI 39
2017
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Marco Cuturi and Justin Solomon, A primer on optimal transport , NIPS Tutorial, 2017
2017
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2017
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Jean Feydy, Benjamin Charlier, François-Xavier Vialard, and Gabriel Peyré, Optimal transport for diffeomorphic registration , MICCAI 2017, 2017
2017
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Hugo Lavenant, Harmonic mappings valued in the Wasserstein space , arXiv:1712.07528 (2017)
2017
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Manish Mandad, David Cohen-Steiner, Leif Kobbelt, Pierre Alliez, and Mathieu Desbrun, Variance-minimizing transport plans for inter-surface mapping , ACM Transactions on Graphics 36
2017
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Gabriel Peyré, Lénaïc Chizat, François-Xavier Vialard, and Justin Solomon, Quantum entropic regularization of matrix-valued optimal transport , European Journal of Applied Mathematics (2017), 1–24
2017
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Gabriel Peyré and Marco Cuturi, Computational optimal transport , Submitted, 2017
2017
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by same author, { \{ Euclidean, metric, and Wasserstein } \} gradient flows: an overview , Bulletin of Mathematical Sciences 7
2017
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Jonah Sherman, Generalized preconditioning and undirected minimum-cost flow , Proc. SODA, SIAM, 2017, pp. 772–780
2017
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Justin Solomon, Computational optimal transport , Snapshots of Modern Mathematics from Oberwolfach (2017), no. 8, 1–15
2017
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Matthew Staib, Sebastian Claici, Justin M Solomon, and Stefanie Jegelka, Parallel streaming Wasserstein barycenters , Advances in Neural Information Processing Systems, 2017, pp. 2644–2655
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2018
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2018
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