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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.04607 |
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Table of 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.