# DOTmark - A Benchmark for Discrete Optimal Transport

arXiv: https://arxiv.org/abs/1610.03368 · HTML: https://mlsanity.com/paper/1610.03368/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Oct 2016.

## Built on by (most cited first, 16 of 16)

- [Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmark](https://mlsanity.com/paper/2106.01954/) (2021)
- [Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey](https://mlsanity.com/paper/2305.05080/) (2023)
- [Efficient and Accurate Optimal Transport with Mirror Descent and Conjugate Gradients](https://mlsanity.com/paper/2307.08507/) (2023)
- [Faster Inference of Flow-Based Generative Models via Improved Data-Noise Coupling](https://mlsanity.com/paper/2603.15279/) (2026)
- [An Accelerated Stochastic Variance-Reduced Algorithm for Entropic Wasserstein Barycenters](https://mlsanity.com/paper/2203.00813/) (2022)
- [A Truncated Newton Method for Optimal Transport](https://mlsanity.com/paper/2504.02067/) (2025)
- [Improving Approximate Optimal Transport Distances using Quantization](https://mlsanity.com/paper/2102.12731/) (2021)
- [PINS: Proximal Iterations with Sparse Newton and Sinkhorn for Optimal Transport](https://mlsanity.com/paper/2502.03749/) (2025)
- [Solving a Special Type of Optimal Transport Problem by a Modified Hungarian Algorithm](https://mlsanity.com/paper/2210.16645/) (2022)
- [Efficient approximation of Earth Mover's Distance Based on Nearest Neighbor Search](https://mlsanity.com/paper/2401.07378/) (2024)
- [Computing the Distance between unbalanced Distributions -- The flat Metric](https://mlsanity.com/paper/2308.01039/) (2023)
- [Quantization-based Bounds on the Wasserstein Metric](https://mlsanity.com/paper/2506.00976/) (2025)
- [Quantifying the noise sensitivity of the Wasserstein metric for images](https://mlsanity.com/paper/2510.01015/) (2025)
- [Field Codes for Distributed Coupling Samplers and Certified Empirical Transport](https://mlsanity.com/paper/2607.27078/) (2026)
- [Annealed Sinkhorn with Momentum: Certified Unregularized Optimal Transport in Linear Memory](https://mlsanity.com/paper/2609.33814/) (2026)
- [GPU-Accelerated Bregman Douglas-Rachford Splitting for Discrete Optimal Transport](https://mlsanity.com/paper/2610.04715/) (2026)

## Abstract (arXiv)

The Wasserstein metric or earth mover's distance (EMD) is a useful tool in statistics, machine learning and computer science with many applications to biological or medical imaging, among others. Especially in the light of increasingly complex data, the computation of these distances via optimal transport is often the limiting factor. Inspired by this challenge, a variety of new approaches to optimal transport has been proposed in recent years and along with these new methods comes the need for a meaningful comparison. In this paper, we introduce a benchmark for discrete optimal transport, called DOTmark, which is designed to serve as a neutral collection of problems, where discrete optimal transport methods can be tested, compared to one another, and brought to their limits on large-scale instances. It consists of a variety of grayscale images, in various resolutions and classes, such as several types of randomly generated images, classical test images and real data from microscopy. Along with the DOTmark we present a survey and a performance test for a cross section of established methods ranging from more traditional algorithms, such as the transportation simplex, to recently developed approaches, such as the shielding neighborhood method, and including also a comparison with commercial solvers.