{"ID":2845454,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.04607","arxiv_id":"2511.04607","title":"Closing the Gap: Efficient Algorithms for Discrete Wasserstein Barycenters","abstract":"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.","short_abstract":"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 researc...","url_abs":"https://arxiv.org/abs/2511.04607","url_pdf":"https://arxiv.org/pdf/2511.04607v1","authors":"[\"Jiaqi Wang\",\"Weijun Xie\"]","published":"2025-11-06T17:58:42Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}