research-article

Truly Tight-in-Δ Bounds for Bipartite Maximal Matching and Variants

Authors:

Sebastian Brandt,

Dennis OlivettiAuthors Info & Claims

PODC '20: Proceedings of the 39th Symposium on Principles of Distributed Computing

Pages 69 - 78

https://doi.org/10.1145/3382734.3405745

Published: 31 July 2020 Publication History

Abstract

In a recent breakthrough result, Balliu et al. [FOCS'19] proved a deterministic Ω(min(Δ, log n/ log log n))-round and a randomized Ω(min(Δ, log log n/ log log log n))-round lower bound for the complexity of the bipartite maximal matching problem on n-node graphs in the LOCAL model of distributed computing. Both lower bounds are asymptotically tight as a function of the maximum degree Δ.

We provide truly tight bounds in Δ for the complexity of bipartite maximal matching and many natural variants, up to and including the additive constant. As a by-product, our results yield a considerably simplified version of the proof by Balliu et al.

We show that our results can be obtained via bounded automatic round elimination, a version of the recent automatic round elimination technique by Brandt [PODC'19] that is particularly suited for automatization from a practical perspective. In this context, our work can be seen as another step towards the automatization of lower bounds in the LOCAL model.

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Cited By

Balliu ABoudier TBrandt SOlivetti DKuznetsov PGelles ROlivetti D(2024)Tight Lower Bounds in the Supported LOCAL ModelProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662798(95-105)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3662158.3662798
Czygrinow AHanćkowiak MRumiński AWitkowski M(2024)Distributed approximation for f-matchingTheoretical Computer Science10.1016/j.tcs.2024.114760(114760)Online publication date: Jul-2024
https://doi.org/10.1016/j.tcs.2024.114760
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
Show More Cited By

Index Terms

Truly Tight-in-Δ Bounds for Bipartite Maximal Matching and Variants
1. Theory of computation
  1. Design and analysis of algorithms
    1. Distributed algorithms

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cover image ACM Conferences

PODC '20: Proceedings of the 39th Symposium on Principles of Distributed Computing

July 2020

539 pages

ISBN:9781450375825

DOI:10.1145/3382734

General Chair:
Yuval Emek
Technion, Israel
,
Program Chair:
Christian Cachin
University of Bern, Switzerland

Copyright © 2020 ACM.

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Published: 31 July 2020

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PODC '20: ACM Symposium on Principles of Distributed Computing

August 3 - 7, 2020

Virtual Event, Italy

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

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Cited By

Balliu ABoudier TBrandt SOlivetti DKuznetsov PGelles ROlivetti D(2024)Tight Lower Bounds in the Supported LOCAL ModelProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662798(95-105)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3662158.3662798
Czygrinow AHanćkowiak MRumiński AWitkowski M(2024)Distributed approximation for f-matchingTheoretical Computer Science10.1016/j.tcs.2024.114760(114760)Online publication date: Jul-2024
https://doi.org/10.1016/j.tcs.2024.114760
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
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
Balliu ABrandt SKuhn FOlivetti DLeonardi SGupta A(2022)Distributed ∆-coloring plays hide-and-seekProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3520027(464-477)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519935.3520027
Balliu ABrandt SKuhn FOlivetti DMilani AWoelfel P(2022)Distributed Edge Coloring in Time Polylogarithmic in ΔProceedings of the 2022 ACM Symposium on Principles of Distributed Computing10.1145/3519270.3538440(15-25)Online publication date: 20-Jul-2022
https://dl.acm.org/doi/10.1145/3519270.3538440
Balliu ABrandt SOlivetti D(2022)Distributed Lower Bounds for Ruling SetsSIAM Journal on Computing10.1137/20M138177051:1(70-115)Online publication date: 8-Feb-2022
https://doi.org/10.1137/20M1381770
Maus YTonoyan T(2022)Linial for listsDistributed Computing10.1007/s00446-022-00424-y35:6(533-546)Online publication date: 17-May-2022
https://doi.org/10.1007/s00446-022-00424-y
Balliu ABrandt SHirvonen JOlivetti DRabie MSuomela J(2021)Lower Bounds for Maximal Matchings and Maximal Independent SetsJournal of the ACM10.1145/346145868:5(1-30)Online publication date: 6-Dec-2021
https://dl.acm.org/doi/10.1145/3461458
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
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