最大流量和最小成本流量的近线性时间算法

IF 11.1 3区计算机科学 Q1 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE

Communications of the ACM Pub Date : 2023-11-17 DOI:10.1145/3610940

Li Chen, Rasmus Kyng, Yang P. Liu, Richard Peng, M. Gutenberg, Sushant Sachdeva

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引用次数: 0

摘要

我们提出了一种算法，它能在 m1+o(1) 时间内，在具有 m 条边和多项式约束积分需求、成本和容量的有向图上计算精确的最大流量和最小成本流量。我们的算法通过 m1+o(1) 个近似无向最小比率循环序列来构建流量，每个循环都是使用新的动态图数据结构在摊销的 mo(1) 时间内计算和处理的。我们的框架扩展到了在 m1+o(1) 时间内运行的算法，用于计算高精度最小化一般边缘可分凸函数的流。这就为一些问题提供了几乎线性时间的算法，包括任意有向无环图上的熵规则化最优传输、矩阵缩放、p-norm 流量和 p-norm 等规回归。

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Almost-Linear-Time Algorithms for Maximum Flow and Minimum-Cost Flow

We present 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 m1+o(1) time. Our algorithm builds the flow through a sequence of m1+o(1) approximate undirected minimum-ratio cycles, each of which is computed and processed in amortized mo(1) time using a new dynamic graph data structure. Our framework extends to algorithms running in m1+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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来源期刊

Communications of the ACM 工程技术-计算机：理论方法

CiteScore

16.10

自引率

0.40%

发文量

276

审稿时长

6-12 weeks

期刊介绍： Communications of the ACM is the leading print and online publication for the computing and information technology fields. Read by computing''s leading professionals worldwide, Communications is recognized as the most trusted and knowledgeable source of industry information for today’s computing professional. Following the traditions of the Communications print magazine, which each month brings its readership of over 100,000 ACM members in-depth coverage of emerging areas of computer science, new trends in information technology, and practical applications, the Communications website brings topical and informative news and material to computing professionals each business day. ACM''s membership includes the IT industry''s most respected leaders and decision makers. Industry leaders have for more than 50 years used the monthly Communications of the ACM magazine as a platform to present and debate various technology implications, public policies, engineering challenges, and market trends. The Communications website continues that practice.