%AChen, Li%AKyng, Rasmus%ALiu, Yang%APeng, Richard%AGutenberg, Maximilian%ASachdeva, Sushant%D2022%I
%K
%MOSTI ID: 10412390
%PMedium: X
%TMaximum Flow and Minimum-Cost Flow in Almost-Linear Time
%XWe 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.
Country unknown/Code not availablehttps://doi.org/10.1109/FOCS54457.2022.00064OSTI-MSA