research-article

Improved deterministic distributed matching via rounding

Author:

Manuela FischerAuthors Info & Claims

Distributed Computing, Volume 33, Issue 3-4

Pages 279 - 291

https://doi.org/10.1007/s00446-018-0344-4

Published: 01 June 2020 Publication History

Abstract

We present improved deterministic distributed algorithms for a number of well-studied matching problems, which are simpler, faster, more accurate, and/or more general than their known counterparts. The common denominator of these results is a deterministic distributed rounding method for certain linear programs, which is the first such rounding method, to our knowledge. A sampling of our end results is as follows:

•

An

O ({log}^{2} Δ \cdot log n)

-round deterministic distributed algorithm for computing a maximal matching, in n-node graphs with maximum degree

Δ

. This is the first improvement in about 20 years over the celebrated

O ({log}^{4} n)

-round algorithm of Hańćkowiak, Karoński, and Panconesi [SODA’98, PODC’99].

•

A deterministic distributed algorithm for computing a

(2 + ε)

-approximation of maximum matching in

O ({log}^{2} Δ \cdot log \frac{1}{ε} + {log}^{} * n)

rounds. This is exponentially faster than the classic

O (Δ + {log}^{*} n)

-round 2-approximation of Panconesi and Rizzi [DIST’01]. With some modifications, the algorithm can also find an almost maximal matching which leaves only an

ε

-fraction of the edges on unmatched nodes.

•

An

O ({log}^{2} Δ \cdot log \frac{1}{ε} \cdot {log}_{1 + ε} W + {log}^{} * n)

-round deterministic distributed algorithm for computing a

(2 + ε)

-approximation of a maximum weighted matching, and also for the more general problem of maximum weighted b-matching. Here, W denotes the maximum normalized weight. These improve over the

O ({log}^{4} n \cdot {log}_{1 + ε} W)

-round

(6 + ε)

-approximation algorithm of Panconesi and Sozio [DIST’10].

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Dahal SSuomela J(2024)Distributed half-integral matching and beyondTheoretical Computer Science10.1016/j.tcs.2023.114278982:COnline publication date: 8-Jan-2024
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Maus Y(2023)Distributed Graph Coloring Made EasyACM Transactions on Parallel Computing10.1145/360589610:4(1-21)Online publication date: 17-Aug-2023
https://dl.acm.org/doi/10.1145/3605896
Ghaffari MGrunau CSaha BServedio R(2023)Faster Deterministic Distributed MIS and Approximate MatchingProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585243(1777-1790)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585243
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Information

Published In

cover image Distributed Computing

Distributed Computing Volume 33, Issue 3-4

Jun 2020

154 pages

ISSN:0178-2770

Issue’s Table of Contents

© Springer-Verlag GmbH Germany, part of Springer Nature 2018.

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 June 2020

Accepted: 27 September 2018

Received: 20 December 2017

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Cited By

Dahal SSuomela J(2024)Distributed half-integral matching and beyondTheoretical Computer Science10.1016/j.tcs.2023.114278982:COnline publication date: 8-Jan-2024
https://dl.acm.org/doi/10.1016/j.tcs.2023.114278
Maus Y(2023)Distributed Graph Coloring Made EasyACM Transactions on Parallel Computing10.1145/360589610:4(1-21)Online publication date: 17-Aug-2023
https://dl.acm.org/doi/10.1145/3605896
Ghaffari MGrunau CSaha BServedio R(2023)Faster Deterministic Distributed MIS and Approximate MatchingProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585243(1777-1790)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585243
Haeupler BHershkowitz DSaranurak TSaha BServedio R(2023)Maximum Length-Constrained Flows and Disjoint Paths: Distributed, Deterministic, and FastProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585202(1371-1383)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585202
Dahal SSuomela J(2023)Distributed Half-Integral Matching and BeyondStructural Information and Communication Complexity10.1007/978-3-031-32733-9_15(339-356)Online publication date: 6-Jun-2023
https://dl.acm.org/doi/10.1007/978-3-031-32733-9_15
Balliu AGhaffari MKuhn FOlivetti DMilani AWoelfel P(2022)Node and Edge Averaged Complexities of Local Graph ProblemsProceedings of the 2022 ACM Symposium on Principles of Distributed Computing10.1145/3519270.3538419(4-14)Online publication date: 20-Jul-2022
https://dl.acm.org/doi/10.1145/3519270.3538419
Ghaffari MPortmann JAgrawal KLee I(2022)Average Awake Complexity of MIS and MatchingProceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3490148.3538566(45-55)Online publication date: 11-Jul-2022
https://dl.acm.org/doi/10.1145/3490148.3538566
Maus YAgrawal KAzar Y(2021)Distributed Graph Coloring Made EasyProceedings of the 33rd ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3409964.3461804(362-372)Online publication date: 6-Jul-2021
https://dl.acm.org/doi/10.1145/3409964.3461804
Turau V(2019)Making Randomized Algorithms Self-stabilizingStructural Information and Communication Complexity10.1007/978-3-030-24922-9_21(309-324)Online publication date: 1-Jul-2019
https://dl.acm.org/doi/10.1007/978-3-030-24922-9_21

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