# Semi-discrete optimal transport - the case p=1

@article{Hartmann2017SemidiscreteOT, title={Semi-discrete optimal transport - the case p=1}, author={Valentin N. Hartmann and Dominic Schuhmacher}, journal={arXiv: Numerical Analysis}, year={2017} }

We consider the problem of finding an optimal transport plan between an absolutely continuous measure $\mu$ on $\mathcal{X} \subset \mathbb{R}^d$ and a finitely supported measure $\nu$ on $\mathbb{R}^d$ when the transport cost is the Euclidean distance. We may think of this problem as closest distance allocation of some ressource continuously distributed over space to a finite number of processing sites with capacity constraints.
This article gives a detailed discussion of the problem…

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