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

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

  • 講者陳力 先生 (喬治亞理工學院)
    邀請人:鐘楷閔
  • 時間2022-09-16 (Fri.) 10:15 – 12:15
  • 地點資訊所新館106演講廳
摘要
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 almost-linear 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 almost-constant time using a new dynamic graph data structure.
Our framework extends to algorithms running in almost-linear 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.
Joint work with Rasmus Kyng, Yang P. Liu, Richard Peng, Maximilian Probst Gutenberg, and Sushant Sachdeva.
https://arxiv.org/abs/2203.00671