research-article

The Distributed Complexity of Locally Checkable Problems on Paths is Decidable

Authors:

Sebastian Brandt,

Dennis Olivetti,

Jukka SuomelaAuthors Info & Claims

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

Pages 262 - 271

https://doi.org/10.1145/3293611.3331606

Published: 16 July 2019 Publication History

Abstract

Consider a computer network that consists of a path with n nodes. The nodes are labeled with inputs from a constant-sized set, and the task is to find output labels from a constant-sized set subject to some local constraints---more formally, we have an LCL (locally checkable labeling) problem. How many communication rounds are needed (in the standard LOCAL model of computing) to solve this problem?

It is well known that the answer is always either O(1) rounds, or Θ(log_⋅ n) rounds, or Θ(n) rounds. In this work we show that this question is decidable (albeit PSPACE-hard): we present an algorithm that, given any LCL problem defined on a path, outputs the distributed computational complexity of this problem and the corresponding asymptotically optimal algorithm.

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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
Chang YStudený JSuomela J(2023)Distributed graph problems through an automata-theoretic lensTheoretical Computer Science10.1016/j.tcs.2023.113710951:COnline publication date: 24-Mar-2023
https://dl.acm.org/doi/10.1016/j.tcs.2023.113710
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
Show More Cited By

Index Terms

The Distributed Complexity of Locally Checkable Problems on Paths is Decidable
1. Theory of computation

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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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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
Chang YStudený JSuomela J(2023)Distributed graph problems through an automata-theoretic lensTheoretical Computer Science10.1016/j.tcs.2023.113710951:COnline publication date: 24-Mar-2023
https://dl.acm.org/doi/10.1016/j.tcs.2023.113710
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 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
Grebík JRozhoň V(2021)Classification of Local Problems on Paths from the Perspective of Descriptive CombinatoricsExtended Abstracts EuroComb 202110.1007/978-3-030-83823-2_89(553-559)Online publication date: 24-Aug-2021
https://doi.org/10.1007/978-3-030-83823-2_89
Chang YStudený JSuomela J(2021)Distributed Graph Problems Through an Automata-Theoretic LensStructural Information and Communication Complexity10.1007/978-3-030-79527-6_3(31-49)Online publication date: 20-Jun-2021
https://doi.org/10.1007/978-3-030-79527-6_3
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
https://dl.acm.org/doi/10.1145/3382734.3405721
Balliu ABrandt SEfron YHirvonen JMaus YOlivetti DSuomela JEmek YCachin C(2020)Brief Announcement: Classification of Distributed Binary Labeling ProblemsProceedings of the 39th Symposium on Principles of Distributed Computing10.1145/3382734.3405703(349-351)Online publication date: 31-Jul-2020
https://dl.acm.org/doi/10.1145/3382734.3405703

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