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Oct 26, 2019 at 20:02 comment added alesia @SoumyaBasu then it is exactly optimal transportation as well as equalities will be attained in the constraints
Oct 26, 2019 at 20:01 comment added alesia @Dirk indeed you need some tricks to avoid rounding problems but if you have a large problem it's still the best method I would say. Solving the exact problem doesn't scale nearly as well except for low dimensional quadratic cost problems where you can do something special
Oct 25, 2019 at 22:22 comment added Soumya Basu Yeah, the minimization was an error. I am interested in the maximization problem. Sorry about the confusion.
Oct 25, 2019 at 19:15 comment added Dirk You are right about the minimizer, but I beg to differ about the Sinkhorn algorithm. It solves a regularized problem and if the regularization problem gets small, the convergence deteriorates (and you get numerical problems and need some more trick to make it work). Also OP is explicitly asking for combinatorial methods.
Oct 25, 2019 at 18:22 history answered alesia CC BY-SA 4.0