{"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/solving-large-multicommodity-network-flow","title":"Solving Large Multicommodity Network Flow Problems on GPUs","arxiv_id":"2501.17996","date":"2025-01-29","proceeding":null,"authors":["Fangzhao Zhang","Stephen Boyd"],"abstract":"We consider the all-pairs multicommodity network flow problem on a network with capacitated edges. The usual treatment keeps track of a separate flow for each source-destination pair on each edge; we rely on a more efficient formulation in which flows with the same destination are aggregated, reducing the number of variables by a factor equal to the size of the network. Problems with hundreds of nodes, with a total number of variables on the order of a million, can be solved using standard generic interior-point methods on CPUs; we focus on GPU-compatible algorithms that can solve such problems much faster, and in addition scale to much larger problems, with up to a billion variables. Our method relies on the primal-dual hybrid gradient algorithm, and exploits several specific features of the problem for efficient GPU computation. Numerical experiments show that our primal-dual multicommodity network flow method accelerates state of the art generic commercial solvers by $100\\times$ to $1000\\times$, and scales to problems that are much larger. We provide an open source implementation of our method.","url_abs":"https://arxiv.org/abs/2501.17996v2","url_pdf":"https://arxiv.org/pdf/2501.17996v2.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":"solving-large-multicommodity-network-flow","repo_url":"https://github.com/cvxgrp/pdmcf","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"jax","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2501.17996","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}