Combinatorial Matrix Classes

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Sinkhorn Distances: Lightspeed Computation of Optimal Transport (2013, background): “As a classic result of linear optimization, the optimum of classical optimal transportation distances is achieved on vertices of U ( r, c ), that is d × d matrices with only up to 2 d − 1 non-zero elements (Brualdi, 2006, § 8.1.3).”
Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning (2019, background): “[9] or specialized auction algorithms [5,6], etc. The set of feasible transportation plans is termed the transportation polytope and displays many useful theoretical properties, which are surveyed in [15]. The need to evaluate Wasserstein distances between increasingly ne-grained histograms has rece”