Discrete & Computational Geometry

, Volume 55, Issue 2, pp 263–283 | Cite as

Discrete Optimal Transport: Complexity, Geometry and Applications

  • Quentin Mérigot
  • Édouard Oudet


In this article, we introduce a new algorithm for solving discrete optimal transport based on iterative resolutions of local versions of the dual linear program. We show a quantitative link between the complexity of this algorithm and the geometry of the underlying measures in the quadratic Euclidean case. This discrete method is then applied to investigate two optimal transport problems with geometric flavor: the regularity of optimal transport plan on oblate ellipsoids, and Alexandrov’s problem of reconstructing a convex set from its Gaussian measure.


Alexandrov problem Optimal transport Brunn–Minkowski inequality 



The authors gratefully acknowledge the support of the French ANR, through the Projects TOMMI (ANR-11-BSO1-014-01) and OPTIFORM (ANR-12-BS01-0007).


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Univ. Grenoble Alpes, LJKGrenobleFrance
  2. 2.CNRS, LJKGrenobleFrance

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