{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-fast-approach-to-optimal-transport-the-back","title":"A fast approach to optimal transport: The back-and-forth method","arxiv_id":"1905.12154","date":"2019-05-29","proceeding":null,"authors":["Matt Jacobs","Flavien Léger"],"abstract":"We present an iterative method to efficiently solve the optimal transportation problem for a class of strictly convex costs which includes quadratic and p-power costs. Given two probability measures supported on a discrete grid with n points, we compute the optimal map using O(n) storage space and O(n log(n)) operations per iteration, with an approximately exponential convergence rate. Our approach allows us to solve optimal transportation problems on spatial grids as large as 4096x4096 and 384x384x384 in a matter of minutes.","url_abs":"https://arxiv.org/abs/1905.12154v2","url_pdf":"https://arxiv.org/pdf/1905.12154v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-fast-approach-to-optimal-transport-the-back","repo_url":"https://github.com/math-jacobs/bfm","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1905.12154","atlas_url":"https://app.syntology.ai/?focus=1905.12154","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}