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

Abstract We introduce a new technique, which we call the boundary method, for solving semi-discrete optimal transport problems with a wide range of cost functions. The boundary method reduces the effective dimension of the problem, thus improving complexity. For cost functions equal to a p -norm with p ∈ ( 1 , ∞ ) , we provide mathematical justification, convergence analysis, and algorithmic development. Our testing supports the boundary method with these p -norms, as well as other, more general cost functions.