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

arXiv: https://arxiv.org/abs/1702.03517 · HTML: https://mlsanity.com/paper/1702.03517/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2017.

## Built on by (most cited first, 2 of 2)

- [PINS: Proximal Iterations with Sparse Newton and Sinkhorn for Optimal Transport](https://mlsanity.com/paper/2502.03749/) (2025)
- [Control Laguerre Tessellation: Semi-discrete Optimal Transport Over Control Systems](https://mlsanity.com/paper/2607.09139/) (2026)

## Abstract (arXiv)

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.