research-article

Improved Distributed Approximate Matching

Authors:

Boaz Patt-Shamir,

Seth PettieAuthors Info & Claims

Journal of the ACM (JACM), Volume 62, Issue 5

Article No.: 38, Pages 1 - 17

https://doi.org/10.1145/2786753

Published: 02 November 2015 Publication History

Abstract

We present distributed network algorithms to compute weighted and unweighted matchings with improved approximation ratios and running times. The computational model is a network of processors exchanging O(log n)-bit messages (the CONGEST model). For unweighted graphs, we give an algorithm providing (1-ϵ)-approximation in O(log n) time for any constant ϵ>0, improving on the classical ½-approximation in Olog n) time of Israeli and Itai [1986]. The time complexity of the algorithm depends on 1⁃ϵ exponentially in the general case, and polynomially in bipartite graphs. For weighted graphs, we present another algorithm which provides (½-ϵ) approximation in general graphs in O(logϵ^-1log n) time, improving on the previously known algorithms which attain (¼-ϵ)-approximation in O(log n) time or ½-approximation in O(n) time. All our algorithms are randomized: the complexity bounds hold both with high probability and for the expected running time.

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Cited By

Gao SCourcoubetis CDuan L(2024)Average-Case Analysis of Greedy Matching for Large-Scale D2D Resource SharingIEEE Transactions on Mobile Computing10.1109/TMC.2023.3278681(1-15)Online publication date: 2024
https://doi.org/10.1109/TMC.2023.3278681
Huang SSu HOshman RNolin AHalldorsson MBalliu A(2023)(1-ϵ)-Approximate Maximum Weighted Matching in poly(1/ϵ, log n) Time in the Distributed and Parallel SettingsProceedings of the 2023 ACM Symposium on Principles of Distributed Computing10.1145/3583668.3594570(44-54)Online publication date: 19-Jun-2023
https://dl.acm.org/doi/10.1145/3583668.3594570
Chang YLi ZOshman RNolin AHalldorsson MBalliu A(2023)The Complexity of Distributed Approximation of Packing and Covering Integer Linear ProgramsProceedings of the 2023 ACM Symposium on Principles of Distributed Computing10.1145/3583668.3594562(32-43)Online publication date: 19-Jun-2023
https://dl.acm.org/doi/10.1145/3583668.3594562
Show More Cited By

Index Terms

Improved Distributed Approximate Matching
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
2. Theory of computation
  1. Models of computation
    1. Concurrency
      1. Parallel computing models

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cover image Journal of the ACM

Journal of the ACM Volume 62, Issue 5

November 2015

368 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/2841330

Editor:
Victor Vianu
University of California, San Diego

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Copyright © 2015 ACM.

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Association for Computing Machinery

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Publication History

Published: 02 November 2015

Accepted: 01 May 2015

Revised: 01 March 2015

Received: 01 August 2014

Published in JACM Volume 62, Issue 5

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Cited By

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https://doi.org/10.1109/TMC.2023.3278681
Huang SSu HOshman RNolin AHalldorsson MBalliu A(2023)(1-ϵ)-Approximate Maximum Weighted Matching in poly(1/ϵ, log n) Time in the Distributed and Parallel SettingsProceedings of the 2023 ACM Symposium on Principles of Distributed Computing10.1145/3583668.3594570(44-54)Online publication date: 19-Jun-2023
https://dl.acm.org/doi/10.1145/3583668.3594570
Chang YLi ZOshman RNolin AHalldorsson MBalliu A(2023)The Complexity of Distributed Approximation of Packing and Covering Integer Linear ProgramsProceedings of the 2023 ACM Symposium on Principles of Distributed Computing10.1145/3583668.3594562(32-43)Online publication date: 19-Jun-2023
https://dl.acm.org/doi/10.1145/3583668.3594562
Limaye G(2023)Envy-freeness and relaxed stability for lower-quotasDiscrete Applied Mathematics10.1016/j.dam.2023.05.011337:C(288-302)Online publication date: 15-Oct-2023
https://dl.acm.org/doi/10.1016/j.dam.2023.05.011
Jowhari H(2023)An estimator for matching size in low arboricity graphs with two applicationsJournal of Combinatorial Optimization10.1007/s10878-022-00929-z45:1Online publication date: 1-Jan-2023
https://dl.acm.org/doi/10.1007/s10878-022-00929-z
KITAMURA NIZUMI T(2022)A Subquadratic-Time Distributed Algorithm for Exact Maximum MatchingIEICE Transactions on Information and Systems10.1587/transinf.2021EDP7083E105.D:3(634-645)Online publication date: 1-Mar-2022
https://doi.org/10.1587/transinf.2021EDP7083
Fischer MMitrović SUitto JLeonardi SGupta A(2022)Deterministic (1+𝜀)-approximate maximum matching with poly(1/𝜀) passes in the semi-streaming model and beyondProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3520039(248-260)Online publication date: 9-Jun-2022
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Agarwal RRajakrishnan SShmoys DMilani AWoelfel P(2022)From Switch Scheduling to Datacenter SchedulingProceedings of the 2022 ACM Symposium on Principles of Distributed Computing10.1145/3519270.3538443(313-323)Online publication date: 20-Jul-2022
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Chang YSu HMilani AWoelfel P(2022)Narrowing the LOCAL-CONGEST Gaps in Sparse Networks via Expander DecompositionsProceedings of the 2022 ACM Symposium on Principles of Distributed Computing10.1145/3519270.3538423(301-312)Online publication date: 20-Jul-2022
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Izumi TKitamura NNaruse TSchwartzman GAgrawal KLee I(2022)Fully Polynomial-Time Distributed Computation in Low-Treewidth GraphsProceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3490148.3538590(11-22)Online publication date: 11-Jul-2022
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