Maximum Flow and Minimum-Cost Flow in Almost-Linear Time

We give 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 m^{1+o(1)} time. Our algorithm builds the flow through a sequence of m^{1+o(1)} approximate undirected minimum-ratio cycle...

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Veröffentlicht in:Proceedings / annual Symposium on Foundations of Computer Science S. 612 - 623
Hauptverfasser: Chen, Li, Kyng, Rasmus, Liu, Yang P., Peng, Richard, Gutenberg, Maximilian Probst, Sachdeva, Sushant
Format: Tagungsbericht
Sprache:Englisch
Veröffentlicht: IEEE 01.10.2022
Schlagworte:
Approximation algorithms
Computer science
Convex optimization
Costs
Data structures
Directed acyclic graph
Directed graphs
Heuristic algorithms
Integral equations
Interior point methods
Maximum flow
Minimum cost flow
ISSN:2575-8454
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Zusammenfassung:We give 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 m^{1+o(1)} time. Our algorithm builds the flow through a sequence of m^{1+o(1)} approximate undirected minimum-ratio cycles, each of which is computed and processed in amortized m^{o(1)} time using a new dynamic graph data structure. Our framework extends to algorithms running in m^{1+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.
ISSN:2575-8454
DOI:10.1109/FOCS54457.2022.00064