# PDOT: a Practical Primal-Dual Algorithm and a GPU-Based Solver for Optimal Transport

arXiv: https://arxiv.org/abs/2407.19689 · HTML: https://mlsanity.com/paper/2407.19689/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jul 2024.

## Built on by (most cited first, 4 of 4)

- [A Provably Convergent and Practical Algorithm for Gromov--Wasserstein Optimal Transport](https://mlsanity.com/paper/2605.04175/) (2026)
- [cuRegOT: A GPU-Accelerated Solver for Entropic-Regularized Optimal Transport](https://mlsanity.com/paper/2605.08793/) (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)

In this paper, we propose a practical primal-dual algorithm with theoretical guarantees and develop a GPU-based solver, which we dub PDOT, for solving large-scale optimal transport problems. Compared to Sinkhorn algorithm or classic LP algorithms, PDOT can achieve high-accuracy solution while efficiently taking advantage of modern computing architecture, i.e., GPUs. On the theoretical side, we show that PDOT has a data-independent widetilde O(mn(m+n)1.5log(frac1ε)) local flop complexity where ε is the desired accuracy, and m and n are the dimension of the original and target distribution, respectively. We further present a data-dependent widetilde O(mn(m+n)3.5Delta + mn(m+n)1.5log(frac1ε)) global flop complexity of PDOT, where Delta is the precision of the data. On the numerical side, we present PDOT, an open-source GPU solver based on the proposed algorithm. Our extensive numerical experiments consistently demonstrate the well balance of PDOT in computing efficiency and accuracy of the solution, compared to Gurobi and Sinkhorn algorithms.