# A Survey on Algorithmic Developments in Optimal Transport Problem with Applications

arXiv: https://arxiv.org/abs/2501.06247 · HTML: https://mlsanity.com/paper/2501.06247/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 40 references that are in the map.
- First posted on arXiv 8 Jan 2025.

## Builds on (most cited first, 16 of 16)

- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measures](https://mlsanity.com/paper/1508.07941/) (2015)
- [Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm](https://mlsanity.com/paper/1802.04367/) (2018)
- [Sliced Wasserstein Generative Models](https://mlsanity.com/paper/1904.05408/) (2019)
- [On the Efficiency of Entropic Regularized Algorithms for Optimal Transport](https://mlsanity.com/paper/1906.01437/) (2019)
- [On Robust Optimal Transport: Computational Complexity and Barycenter Computation](https://mlsanity.com/paper/2102.06857/) (2021)
- [Towards Optimal Running Times for Optimal Transport](https://mlsanity.com/paper/1810.07717/) (2018)
- [Approximating optimal transport with linear programs](https://mlsanity.com/paper/1810.05957/) (2018)
- [A Graph Theoretic Additive Approximation of Optimal Transport](https://mlsanity.com/paper/1905.11830/) (2019)
- [Accelerated Bregman Primal-Dual methods applied to Optimal Transport and Wasserstein Barycenter problems](https://mlsanity.com/paper/2203.00802/) (2022)
- [An Accelerated Stochastic Variance-Reduced Algorithm for Entropic Wasserstein Barycenters](https://mlsanity.com/paper/2203.00813/) (2022)
- [Fast Computation of Optimal Transport via Entropy-Regularized Extragradient Methods](https://mlsanity.com/paper/2301.13006/) (2023)
- [OTW: Optimal Transport Warping for Time Series](https://mlsanity.com/paper/2306.00620/) (2023)
- [The Monge-Kantorovich problem for distributions and applications](https://mlsanity.com/paper/1312.5453/) (2013)
- [An Integrated Cyber-Physical Risk Assessment Framework for Worst-Case Attacks in Industrial Control Systems](https://mlsanity.com/paper/2304.07363/) (2023)
- [Two-echelon Electric Vehicle Routing Problem in Parcel Delivery: A Literature Review](https://mlsanity.com/paper/2412.19395/) (2024)

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

- [Grasp2Grasp: Vision-Based Dexterous Grasp Translation via Schr"odinger Bridges](https://mlsanity.com/paper/2506.02489/) (2025)
- [UG-UMRE: Uncertainty-Guided Modality Augmentation and Distributional Calibration for Unified Multimodal Relation Extraction](https://mlsanity.com/paper/2608.04949/) (2026)
- [Unlocking Geodesic Gromov-Wasserstein Distances for 3D Modeling](https://mlsanity.com/paper/2609.32824/) (2026)
- [Exact Optimal Transport by Matching](https://mlsanity.com/paper/2610.04085/) (2026)

## Abstract (arXiv)

Optimal Transport (OT) has established itself as a robust framework for quantifying differences between distributions, with applications that span fields such as machine learning, data science, and computer vision. This paper offers a detailed examination of the OT problem, beginning with its theoretical foundations, including the classical formulations of Monge and Kantorovich and their extensions to modern computational techniques. It explores cutting-edge algorithms, including Sinkhorn iterations, primal-dual strategies, and reduction-based approaches, emphasizing their efficiency and scalability in addressing high-dimensional problems. The paper also highlights emerging trends, such as integrating OT into machine learning frameworks, the development of novel problem variants, and ongoing theoretical advancements. Applications of OT are presented across a range of domains, with particular attention to its innovative application in time series data analysis via Optimal Transport Warping (OTW), a robust alternative to methods like Dynamic Time Warping. Despite the significant progress made, challenges related to scalability, robustness, and ethical considerations remain, necessitating further research. The paper underscores OT's potential to bridge theoretical depth and practical utility, fostering impactful advancements across diverse disciplines.