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Max flows in O(nm) time, or better

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James B. OrlinAuthors Info & Claims

STOC '13: Proceedings of the forty-fifth annual ACM symposium on Theory of Computing

Pages 765 - 774

https://doi.org/10.1145/2488608.2488705

Published: 01 June 2013 Publication History

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Abstract

In this paper, we present improved polynomial time algorithms for the max flow problem defined on sparse networks with n nodes and m arcs. We show how to solve the max flow problem in O(nm + m^31/16 log² n) time. In the case that m = O(n^1.06), this improves upon the best previous algorithm due to King, Rao, and Tarjan, who solved the max flow problem in O(nm log_{m/(n log n)}n) time. This establishes that the max flow problem is solvable in O(nm) time for all values of n and m. In the case that m = O(n), we improve the running time to O(n²/ log n).

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Cited By

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Cáceres MCairo MGrigorjew AKhan SMumey BRizzi RTomescu AWilliams L(2024)Width Helps and Hinders Splitting FlowsACM Transactions on Algorithms10.1145/364182020:2(1-20)Online publication date: 13-Mar-2024
https://dl.acm.org/doi/10.1145/3641820
Wickrama Arachchi CKumpulainen ITatti NBaeza-Yates RBonchi F(2024)Dense Subgraph Discovery Meets Strong Triadic ClosureProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining10.1145/3637528.3671697(3334-3344)Online publication date: 25-Aug-2024
https://dl.acm.org/doi/10.1145/3637528.3671697
Zhong HZhang YYan CXuan ZYu TZhang JYing SGao Y(2024)Penalized Flow Hypergraph Local ClusteringIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2023.331901936:5(2110-2125)Online publication date: May-2024
https://doi.org/10.1109/TKDE.2023.3319019
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Index Terms

Max flows in O(nm) time, or better
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
      2. Network flows
2. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis
      1. Network flows

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Published In

STOC '13: Proceedings of the forty-fifth annual ACM symposium on Theory of Computing

June 2013

998 pages

ISBN:9781450320290

DOI:10.1145/2488608

General Chairs:
Dan Boneh
Stanford University, USA
,
Tim Roughgarden
Stanford University, USA
,
Program Chair:
Joan Feigenbaum
Yale University, USA

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Published: 01 June 2013

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STOC'13: Symposium on Theory of Computing

June 1 - 4, 2013

California, Palo Alto, USA

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STOC '13 Paper Acceptance Rate 100 of 360 submissions, 28%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

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Cáceres MCairo MGrigorjew AKhan SMumey BRizzi RTomescu AWilliams L(2024)Width Helps and Hinders Splitting FlowsACM Transactions on Algorithms10.1145/364182020:2(1-20)Online publication date: 13-Mar-2024
https://dl.acm.org/doi/10.1145/3641820
Wickrama Arachchi CKumpulainen ITatti NBaeza-Yates RBonchi F(2024)Dense Subgraph Discovery Meets Strong Triadic ClosureProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining10.1145/3637528.3671697(3334-3344)Online publication date: 25-Aug-2024
https://dl.acm.org/doi/10.1145/3637528.3671697
Zhong HZhang YYan CXuan ZYu TZhang JYing SGao Y(2024)Penalized Flow Hypergraph Local ClusteringIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2023.331901936:5(2110-2125)Online publication date: May-2024
https://doi.org/10.1109/TKDE.2023.3319019
Macktoobian MShu ZZhao Q(2024)Traffic Divergence Theory: An Analysis Formalism for Dynamic NetworksIEEE Access10.1109/ACCESS.2024.338343612(67512-67524)Online publication date: 2024
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Boeckmann JThielen C(2024) A -approximation for network flow interdiction with unit costs Discrete Applied Mathematics10.1016/j.dam.2021.07.008354(58-71)Online publication date: Sep-2024
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