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arXiv · 1702.03517

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

Luca Dieci·J. D. Walsh III
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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 in (1,infinity), 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.

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Luca Dieci, J. D. Walsh III. 2017-02-12. The boundary method for semi-discrete optimal transport partitions and Wasserstein distance computation. https://doi.org/10.1016/j.cam.2018.12.034

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