research-article

A scaling algorithm for maximum weight matching in bipartite graphs

Authors:

Hsin-Hao SuAuthors Info & Claims

SODA '12: Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete algorithms

Pages 1413 - 1424

Published: 17 January 2012 Publication History

Abstract

Given a weighted bipartite graph, the maximum weight matching (MWM) problem is to find a set of vertex-disjoint edges with maximum weight. We present a new scaling algorithm that runs in O(m√n log N) time, when the weights are integers within the range of [0,N]. The result improves the previous bounds of O(Nm√n) by Gabow and O(m√n log (nN)) by Gabow and Tarjan over 20 years ago. Our improvement draws ideas from a not widely known result, the primal method by Balinski and Gomory.

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Cited By

Gupta HCurran MZhan CHan DFeldmann A(2020)Near-optimal multihop scheduling in general circuit-switched networksProceedings of the 16th International Conference on emerging Networking EXperiments and Technologies10.1145/3386367.3432589(31-45)Online publication date: 23-Nov-2020
https://dl.acm.org/doi/10.1145/3386367.3432589
Duan RPettie SSu H(2018)Scaling Algorithms for Weighted Matching in General GraphsACM Transactions on Algorithms10.1145/315530114:1(1-35)Online publication date: 3-Jan-2018
https://dl.acm.org/doi/10.1145/3155301
Bojja Venkatakrishnan SAlizadeh MViswanath P(2018)Costly circuits, submodular schedules and approximate Carathéodory TheoremsQueueing Systems: Theory and Applications10.1007/s11134-017-9546-x88:3-4(311-347)Online publication date: 1-Apr-2018
https://dl.acm.org/doi/10.1007/s11134-017-9546-x
Show More Cited By

Index Terms

A scaling algorithm for maximum weight matching in bipartite graphs
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis
      1. Routing and network design problems

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cover image ACM Other conferences

SODA '12: Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete algorithms

January 2012

1764 pages

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Kyoto University: Kyoto University

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SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 17 January 2012

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SODA '12

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Kyoto University

SODA '12: ACM-SIAM Symposium on Discrete Algorithms

January 17 - 19, 2012

Kyoto, Japan

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Overall Acceptance Rate 411 of 1,322 submissions, 31%

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Cited By

Gupta HCurran MZhan CHan DFeldmann A(2020)Near-optimal multihop scheduling in general circuit-switched networksProceedings of the 16th International Conference on emerging Networking EXperiments and Technologies10.1145/3386367.3432589(31-45)Online publication date: 23-Nov-2020
https://dl.acm.org/doi/10.1145/3386367.3432589
Duan RPettie SSu H(2018)Scaling Algorithms for Weighted Matching in General GraphsACM Transactions on Algorithms10.1145/315530114:1(1-35)Online publication date: 3-Jan-2018
https://dl.acm.org/doi/10.1145/3155301
Bojja Venkatakrishnan SAlizadeh MViswanath P(2018)Costly circuits, submodular schedules and approximate Carathéodory TheoremsQueueing Systems: Theory and Applications10.1007/s11134-017-9546-x88:3-4(311-347)Online publication date: 1-Apr-2018
https://dl.acm.org/doi/10.1007/s11134-017-9546-x
Duan RPettie SSu HKlein P(2017)Scaling algorithms for weighted matching in general graphsProceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3039686.3039736(781-800)Online publication date: 16-Jan-2017
https://dl.acm.org/doi/10.5555/3039686.3039736
Cohen MMądry ASankowski PVladu AKlein P(2017)Negative-weight shortest paths and unit capacity minimum cost flow in Õ(m10/7 log W) timeProceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3039686.3039734(752-771)Online publication date: 16-Jan-2017
https://dl.acm.org/doi/10.5555/3039686.3039734
Deng DKim AMadden SStonebraker M(2017)SilkMothProceedings of the VLDB Endowment10.14778/3115404.311541310:10(1082-1093)Online publication date: 1-Jun-2017
https://dl.acm.org/doi/10.14778/3115404.3115413
Bojja Venkatakrishnan SAlizadeh MViswanath P(2016)Costly Circuits, Submodular Schedules and Approximate Carathéodory TheoremsACM SIGMETRICS Performance Evaluation Review10.1145/2964791.290147944:1(75-88)Online publication date: 14-Jun-2016
https://dl.acm.org/doi/10.1145/2964791.2901479
Bojja Venkatakrishnan SAlizadeh MViswanath PAlouf SJean-Marie AHegde NProutière A(2016)Costly Circuits, Submodular Schedules and Approximate Carathéodory TheoremsProceedings of the 2016 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Science10.1145/2896377.2901479(75-88)Online publication date: 14-Jun-2016
https://dl.acm.org/doi/10.1145/2896377.2901479
Duan RPettie S(2014)Linear-Time Approximation for Maximum Weight MatchingJournal of the ACM10.1145/252998961:1(1-23)Online publication date: 1-Jan-2014
https://dl.acm.org/doi/10.1145/2529989
Huang CKavitha T(2012)Efficient algorithms for maximum weight matchings in general graphs with small edge weightsProceedings of the twenty-third annual ACM-SIAM symposium on Discrete algorithms10.5555/2095116.2095226(1400-1412)Online publication date: 17-Jan-2012
https://dl.acm.org/doi/10.5555/2095116.2095226

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