research-article

Hardness of Minimal Symmetry Breaking in Distributed Computing

Authors:

Dennis Olivetti,

Jukka SuomelaAuthors Info & Claims

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

Pages 369 - 378

https://doi.org/10.1145/3293611.3331605

Published: 16 July 2019 Publication History

Abstract

A graph is weakly 2-colored if the nodes are labeled with colors black and white such that each black node is adjacent to at least one white node and vice versa. In this work we study the distributed computational complexity of weak 2-coloring in the standard łocal model of distributed computing, and how it is related to the distributed computational complexity of other graph problems.

First, we show that weak 2-coloring is a minimal distributed symmetry-breaking problem for regular even-degree trees and high-girth graphs: if there is any non-trivial locally checkable labeling problem that is solvable in o(log^⋅ n) rounds with a distributed graph algorithm in the middle of a regular even-degree tree, then weak 2-coloring is also solvable in o(log^⋅ n) rounds there.

Second, we prove a tight lower bound of Ω(log ^⋅ n) for the distributed computational complexity of weak 2-coloring in regular trees; previously only a lower bound of Ω n(log log^⋅ n) was known. By minimality, the same lower bound holds for any non-trivial locally checkable problem inside regular even-degree trees.

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Cited By

Balliu ABrandt SKuhn FOlivetti DSchmid GKuznetsov PGelles ROlivetti D(2024)Completing the Node-Averaged Complexity Landscape of LCLs on TreesProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662773(369-379)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3662158.3662773
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
Grunau CRozhoň VBrandt SMilani AWoelfel P(2022)The Landscape of Distributed Complexities on Trees and BeyondProceedings of the 2022 ACM Symposium on Principles of Distributed Computing10.1145/3519270.3538452(37-47)Online publication date: 20-Jul-2022
https://dl.acm.org/doi/10.1145/3519270.3538452
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Index Terms

Hardness of Minimal Symmetry Breaking in Distributed Computing
1. Theory of computation
  1. Computational complexity and cryptography
    1. Complexity classes
  2. Models of computation
    1. Concurrency
      1. Distributed computing models

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Abstract
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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.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Published: 16 July 2019

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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

Balliu ABrandt SKuhn FOlivetti DSchmid GKuznetsov PGelles ROlivetti D(2024)Completing the Node-Averaged Complexity Landscape of LCLs on TreesProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662773(369-379)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3662158.3662773
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
Grunau CRozhoň VBrandt SMilani AWoelfel P(2022)The Landscape of Distributed Complexities on Trees and BeyondProceedings of the 2022 ACM Symposium on Principles of Distributed Computing10.1145/3519270.3538452(37-47)Online publication date: 20-Jul-2022
https://dl.acm.org/doi/10.1145/3519270.3538452
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
Balliu ABrandt SChang YOlivetti DStudený JSuomela JTereshchenko A(2022)Locally checkable problems in rooted treesDistributed Computing10.1007/s00446-022-00435-936:3(277-311)Online publication date: 22-Aug-2022
https://doi.org/10.1007/s00446-022-00435-9
Balliu ABrandt SOlivetti DStudený JSuomela JTereshchenko AMiller ACensor-Hillel K(2021)Locally Checkable Problems in Rooted TreesProceedings of the 2021 ACM Symposium on Principles of Distributed Computing10.1145/3465084.3467934(263-272)Online publication date: 21-Jul-2021
https://dl.acm.org/doi/10.1145/3465084.3467934
Balliu ABrandt SKuhn FOlivetti DMiller ACensor-Hillel K(2021)Improved Distributed Lower Bounds for MIS and Bounded (Out-)Degree Dominating Sets in TreesProceedings of the 2021 ACM Symposium on Principles of Distributed Computing10.1145/3465084.3467901(283-293)Online publication date: 21-Jul-2021
https://dl.acm.org/doi/10.1145/3465084.3467901
Brandt SOlivetti DEmek YCachin C(2020)Truly Tight-in-Δ Bounds for Bipartite Maximal Matching and VariantsProceedings of the 39th Symposium on Principles of Distributed Computing10.1145/3382734.3405745(69-78)Online publication date: 31-Jul-2020
https://dl.acm.org/doi/10.1145/3382734.3405745
Rosenbaum WSuomela JEmek YCachin C(2020)Seeing Far vs. Seeing Wide: Volume Complexity of Local Graph ProblemsProceedings of the 39th Symposium on Principles of Distributed Computing10.1145/3382734.3405721(89-98)Online publication date: 31-Jul-2020
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Olivetti DEmek YCachin C(2020)Brief Announcement: Round eliminator: a tool for automatic speedup simulationProceedings of the 39th Symposium on Principles of Distributed Computing10.1145/3382734.3405694(352-354)Online publication date: 31-Jul-2020
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