Corpus ID: 211082751

Revisiting Fixed Support Wasserstein Barycenter: Computational Hardness and Efficient Algorithms

@article{Lin2020RevisitingFS,
  title={Revisiting Fixed Support Wasserstein Barycenter: Computational Hardness and Efficient Algorithms},
  author={Tianyi Lin and Nhat Ho and X. Chen and Marco Cuturi and Michael I. Jordan},
  journal={ArXiv},
  year={2020},
  volume={abs/2002.04783}
}
We study the fixed-support Wasserstein barycenter problem (FS-WBP), which consists in computing the Wasserstein barycenter of m discrete probability measures supported on a finite metric space of size n. We show first that the constraint matrix arising from the linear programming (LP) representation of the FS-WBP is totally unimodular when m ≥ 3 and n = 2, but not totally unimodular when m ≥ 3 and n ≥ 3. This result answers an open problem, since it shows that the FS-WBP is not a minimum-cost… Expand

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