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Parallel and Distributed Expander Decomposition: Simple, Fast, and Near-Optimal

https://doi.org/10.1137/1.9781611978322.53

Chen, Daoyuan; Meierhans, Simon; Gutenberg, Maximilian Probst; Saranurak, Thatchaphol (January 2025, Society for Industrial and Applied Mathematics)

Free, publicly-accessible full text available January 1, 2026
Incremental Approximate Maximum Flow on Undirected Graphs in Subpolynomial Update Time

van_den_Brand, Jan; Chen, Li; Kyng, Rasmus; Liu, Yang P; Peng, Richard; Gutenberg, Maximilian Probst; Sachdeva, Sushant; Sidford, Aaron (January 2024, SODA 2024)

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A Deterministic Almost-Linear Time Algorithm for Minimum-Cost Flow

https://doi.org/10.1109/FOCS57990.2023.00037

Brand, Jan Van; Chen, Li; Peng, Richard; Kyng, Rasmus; Liu, Yang P.; Gutenberg, Maximilian Probst; Sachdeva, Sushant; Sidford, Aaron (November 2023, IEEE)

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

https://doi.org/10.1109/FOCS54457.2022.00064

Chen, Li; Kyng, Rasmus; Liu, Yang P.; Peng, Richard; Gutenberg, Maximilian Probst; Sachdeva, Sushant (October 2022, 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS))

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.
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