Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.04607 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908634082967552 |
|---|---|
| author | Wang, Jiaqi Xie, Weijun |
| author_facet | Wang, Jiaqi Xie, Weijun |
| contents | The Wasserstein barycenter problem seeks a probability measure that minimizes the weighted average of the Wasserstein distances to a given collection of probability measures. We study the discrete setting, where each measure has finite support-- a regime that frequently arises in machine learning and operations research. The discrete Wasserstein barycenter problem is known to be NP-hard, which motivates us to study approximation algorithms with provable guarantees. The best-known algorithm to date achieves an approximation ratio of two. We close this gap by developing a polynomial-time approximation scheme (PTAS) for the discrete Wasserstein barycenter problem that generalizes and improves upon the 2-approximation method. In addition, for the special case of equally weighted measures, we obtain a strictly tighter approximation guarantee. Numerical experiments show that the proposed algorithms are computationally efficient and produce near-optimal barycenter solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04607 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Closing the Gap: Efficient Algorithms for Discrete Wasserstein Barycenters Wang, Jiaqi Xie, Weijun Optimization and Control The Wasserstein barycenter problem seeks a probability measure that minimizes the weighted average of the Wasserstein distances to a given collection of probability measures. We study the discrete setting, where each measure has finite support-- a regime that frequently arises in machine learning and operations research. The discrete Wasserstein barycenter problem is known to be NP-hard, which motivates us to study approximation algorithms with provable guarantees. The best-known algorithm to date achieves an approximation ratio of two. We close this gap by developing a polynomial-time approximation scheme (PTAS) for the discrete Wasserstein barycenter problem that generalizes and improves upon the 2-approximation method. In addition, for the special case of equally weighted measures, we obtain a strictly tighter approximation guarantee. Numerical experiments show that the proposed algorithms are computationally efficient and produce near-optimal barycenter solutions. |
| title | Closing the Gap: Efficient Algorithms for Discrete Wasserstein Barycenters |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2511.04607 |