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Main Authors: Zhang, Fangzhao, Boyd, Stephen
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2501.17996
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author Zhang, Fangzhao
Boyd, Stephen
author_facet Zhang, Fangzhao
Boyd, Stephen
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2501_17996
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Solving Large Multicommodity Network Flow Problems on GPUs
Zhang, Fangzhao
Boyd, Stephen
Optimization and Control
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.
title Solving Large Multicommodity Network Flow Problems on GPUs
topic Optimization and Control
url https://arxiv.org/abs/2501.17996