# The GenCol algorithm for high-dimensional optimal transport: general formulation and application to barycenters and Wasserstein splines

arXiv: https://arxiv.org/abs/2209.09081 · HTML: https://mlsanity.com/paper/2209.09081/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 25 references that are in the map.
- First posted on arXiv 19 Sep 2022.

## Builds on (most cited first, 12 of 12)

- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems](https://mlsanity.com/paper/1610.06519/) (2016)
- [Multi-marginal optimal transport: theory and applications](https://mlsanity.com/paper/1406.0026/) (2014)
- [A Smoothed Dual Approach for Variational Wasserstein Problems](https://mlsanity.com/paper/1503.02533/) (2015)
- [Second order models for optimal transport and cubic splines on the Wasserstein space](https://mlsanity.com/paper/1801.04144/) (2018)
- [Measure-valued spline curves: an optimal transport viewpoint](https://mlsanity.com/paper/1801.03186/) (2018)
- [A Fast Globally Linearly Convergent Algorithm for the Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1809.04249/) (2018)
- [Randomised Wasserstein Barycenter Computation: Resampling with Statistical Guarantees](https://mlsanity.com/paper/2012.06397/) (2020)
- [Genetic column generation: Fast computation of high-dimensional multi-marginal optimal transport problems](https://mlsanity.com/paper/2103.12624/) (2021)
- [A simple counterexample to the Monge ansatz in multi-marginal optimal transport, convex geometry of the set of Kantorovich plans, and the Frenkel-Kontorova model](https://mlsanity.com/paper/1808.04318/) (2018)
- [Non-existence of optimal transport maps for the multi-marginal repulsive harmonic cost](https://mlsanity.com/paper/1805.00417/) (2018)

## Built on by (most cited first, 1 of 1)

- [Genetic Column Generation for Computing Lower Bounds for Adversarial Classification](https://mlsanity.com/paper/2406.08331/) (2024)

## Abstract (arXiv)

We extend the recently introduced genetic column generation algorithm for high-dimensional multi-marginal optimal transport from symmetric to general problems. We use the algorithm to calculate accurate mesh-free Wasserstein barycenters and cubic Wasserstein splines.