Yang Liu (Stanford)
Monday, March 14, 2022
Klaus 1116 - 11:00 am
Title: Maximum Flow and Minimum-Cost Flow in Almost-Linear Time
Abstract: 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 dynamic data structure.
Our framework extends to an algorithm running in $m^{1+o(1)}$ time for computing flows that minimize general edge-separable convex functions to high accuracy. This gives an almost-linear time algorithm for several problems including entropy-regularized optimal transport, matrix scaling, $p$-norm flows, and isotonic regression.
Joint work with Li Chen, Rasmus Kyng, Richard Peng, Maximilian Probst Gutenberg, and Sushant Sachdeva.
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