• Corpus ID: 53703756

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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