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We introduce a new technique, which we call the boundary method, for solvingsemi-discrete optimal transport problems with a wide range of cost functions.The boundary method reduces the effective dimension of the problem, thusimproving complexity. For cost functions equal to a p-norm with p in(1,infinity), we provide mathematical justification, convergence analysis, andalgorithmic development. Our testing supports the boundary method with thesep-norms, as well as other, more general cost functions.

The boundary method for semi-discrete optimal transport partitions and Wasserstein distance computation