research-article

Weighted Matchings via Unweighted Augmentations

Authors:

Buddhima Gamlath,

Slobodan Mitrovic,

Ola SvenssonAuthors Info & Claims

PODC '19: Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing

Pages 491 - 500

https://doi.org/10.1145/3293611.3331603

Published: 16 July 2019 Publication History

Abstract

We design a generic method to reduce the task of finding weighted matchings to that of finding short augmenting paths in unweighted graphs. This method enables us to provide efficient implementations for approximating weighted matchings in the massively parallel computation (MPC) model and in the streaming model.

For the MPC and the multi-pass streaming model, we show that any algorithm computing a (1-δ)-approximate unweighted matching in bipartite graphs can be translated into an algorithm that computes a (1-(ε(δ))-approximate maximum weighted matching. Furthermore, this translation incurs only a constant factor (that depends on ε > 0) overhead in the complexity. Instantiating this with the current best MPC algorithm for unweighted matching yields a (1 - ε)-approximation algorithm for maximum weighted matching that uses O_ε(log log n) rounds, O(m/n) machines per round, and O(npoly(logn)) memory per machine. This improves upon the previous best approximation guarantee of (1/2-ε) for weighted graphs. In the context of single-pass streaming with random edge arrivals, our techniques yield a (1/2+c)-approximation algorithm thus breaking the natural barrier of 1/2.

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Cited By

Assadi S(2023)Recent Advances in Multi-Pass Graph Streaming Lower BoundsACM SIGACT News10.1145/3623800.362380854:3(48-75)Online publication date: 11-Sep-2023
https://dl.acm.org/doi/10.1145/3623800.3623808
Behnezhad SHajiaghayi MHarris D(2023)Exponentially Faster Massively Parallel Maximal MatchingJournal of the ACM10.1145/361736070:5(1-18)Online publication date: 11-Oct-2023
https://dl.acm.org/doi/10.1145/3617360
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
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Index Terms

Weighted Matchings via Unweighted Augmentations
1. Theory of computation
  1. Design and analysis of algorithms
    1. Parallel algorithms
      1. Massively parallel algorithms
      2. Vector / streaming algorithms
  2. Models of computation
    1. Streaming models

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cover image ACM Conferences

PODC '19: Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing

July 2019

563 pages

ISBN:9781450362177

DOI:10.1145/3293611

General Chair:
Peter Robinson
City University of Hong Kong
,
Program Chair:
Faith Ellen
University of Toronto, Canada

Copyright © 2019 ACM.

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Published: 16 July 2019

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European Research Council
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

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PODC '19

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PODC '19: ACM Symposium on Principles of Distributed Computing

July 29 - August 2, 2019

Toronto ON, Canada

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PODC '19 Paper Acceptance Rate 48 of 173 submissions, 28%;

Overall Acceptance Rate 740 of 2,477 submissions, 30%

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Cited By

Assadi S(2023)Recent Advances in Multi-Pass Graph Streaming Lower BoundsACM SIGACT News10.1145/3623800.362380854:3(48-75)Online publication date: 11-Sep-2023
https://dl.acm.org/doi/10.1145/3623800.3623808
Behnezhad SHajiaghayi MHarris D(2023)Exponentially Faster Massively Parallel Maximal MatchingJournal of the ACM10.1145/361736070:5(1-18)Online publication date: 11-Oct-2023
https://dl.acm.org/doi/10.1145/3617360
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
Assadi SSundaresan J(2023)Hidden Permutations to the Rescue: Multi-Pass Streaming Lower Bounds for Approximate Matchings2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00058(909-932)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00058
Bernstein A(2023)Improved Bounds for Matching in Random-Order StreamsTheory of Computing Systems10.1007/s00224-023-10155-7Online publication date: 12-Dec-2023
https://doi.org/10.1007/s00224-023-10155-7
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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Ghaffari MGrunau CMitrović SAgrawal KLee I(2022)Massively Parallel Algorithms for b-MatchingProceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3490148.3538589(35-44)Online publication date: 11-Jul-2022
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Fernando RGelles YKomargodski IShi E(2022)Maliciously Secure Massively Parallel Computation for All-but-One CorruptionsAdvances in Cryptology – CRYPTO 202210.1007/978-3-031-15802-5_24(688-718)Online publication date: 12-Oct-2022
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Biswas ADory MGhaffari MMitrović SNazari YAgrawal KAzar Y(2021)Massively Parallel Algorithms for Distance Approximation and SpannersProceedings of the 33rd ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3409964.3461784(118-128)Online publication date: 6-Jul-2021
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Bernstein ADudeja ALangley ZKhuller SVassilevska Williams V(2021)A framework for dynamic matching in weighted graphsProceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing10.1145/3406325.3451113(668-681)Online publication date: 15-Jun-2021
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