Almost-Linear-Time Algorithms for Maximum Flow and Minimum-Cost Flow
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Date
2023-12
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Journal Article
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yes
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Abstract
We present an algorithm that computes exact maximum flows and minimum-cost flows on directed graphs with m edges and polynomially bounded integral demands, costs, and capacities in m1+o(1) time. Our algorithm builds the flow through a sequence of m1+o(1) approximate undirected minimum-ratio cycles, each of which is computed and processed in amortized mo(1) time using a new dynamic graph data structure.
Our framework extends to algorithms running in m1+o(1) time for computing flows that minimize general edge-separable convex functions to high accuracy. This gives almost-linear time algorithms for several problems including entropy-regularized optimal transport, matrix scaling, p-norm flows, and p-norm isotonic regression on arbitrary directed acyclic graphs.
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published
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66 (12)
Pages / Article No.
85 - 92
Publisher
Association for Computing Machinery
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Organisational unit
09687 - Kyng, Rasmus / Kyng, Rasmus
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Funding
204787 - Algorithms and complexity for high-accuracy flows and convex optimization (SNF)