research-article

Brief Announcement: Classification of Distributed Binary Labeling Problems

Authors:

Sebastian Brandt,

Dennis Olivetti,

Jukka SuomelaAuthors Info & Claims

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

Pages 349 - 351

https://doi.org/10.1145/3382734.3405703

Published: 31 July 2020 Publication History

Abstract

We present a complete classification of the deterministic distributed time complexity for a family of graph problems: binary labeling problems in trees in the usual LOCAL model of distributed computing. These are locally checkable problems that can be encoded with an alphabet of size two in the edge labeling formalism. Examples of binary labeling problems include sinkless orientation, sinkless and sourceless orientation, 2-vertex coloring, and perfect matching. We show that the complexity of any such problem is in one of the following classes: O(1), Θ(log n), Θ(n), or unsolvable. Furthermore, given the description of any binary labeling problem, we can easily determine in which of the four classes it is and what is an asymptotically optimal algorithm for solving it.

References

[1]

Alkida Balliu, Sebastian Brandt, Yi-Jun Chang, Dennis Olivetti, Mikaël Rabie, and Jukka Suomela. 2019. The Distributed Complexity of Locally Checkable Problems on Paths is Decidable. In Proc. 38th ACM Symposium on Principles of Distributed Computing (PODC 2019). ACM Press, 262--271. arXiv:1811.01672

Digital Library

[2]

Alkida Balliu, Sebastian Brandt, Juho Hirvonen, Dennis Olivetti, Mikaël Rabie, and Jukka Suomela. 2019. Lower bounds for maximal matchings and maximal independent sets. In Proc. 60th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2019). IEEE, 481--497. arXiv:1901.02441

[3]

Alkida Balliu, Sebastian Brandt, and Dennis Olivetti. 2020. Distributed Lower Bounds for Ruling Sets. arXiv:2004.08282 http://arxiv.org/abs/2004.08282

[4]

Alkida Balliu, Sebastian Brandt, Dennis Olivetti, and Jukka Suomela. 2018. Almost global problems in the LOCAL model. In Proc. 32nd International Symposium on Distributed Computing (DISC 2018) (Leibniz International Proceedings in Informatics (LIPIcs)). Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 9:1--9:16.

[5]

Alkida Balliu, Juho Hirvonen, Janne H Korhonen, Tuomo Lempiäinen, Dennis Olivetti, and Jukka Suomela. 2018. New classes of distributed time complexity. In Proc. 50th ACM Symposium on Theory of Computing (STOC 2018). ACM Press, 1307--1318.

Digital Library

[6]

Sebastian Brandt. 2019. An Automatic Speedup Theorem for Distributed Problems. In Proc. 38th ACM Symposium on Principles of Distributed Computing (PODC 2019). ACM Press, 379--388. arXiv:1902.09958

Digital Library

[7]

Sebastian Brandt, Orr Fischer, Juho Hirvonen, Barbara Keller, Tuomo Lempiäinen, Joel Rybicki, Jukka Suomela, and Jara Uitto. 2016. A lower bound for the distributed Lovász local lemma. In Proc. 48th ACM Symposium on Theory of Computing (STOC 2016). ACM Press, 479--488.

Digital Library

[8]

Sebastian Brandt, Juho Hirvonen, Janne H Korhonen, Tuomo Lempiäinen, Patric R J Östergård, Christopher Purcell, Joel Rybicki, Jukka Suomela, and Przemysław Uznański. 2017. LCL problems on grids. In Proc. 36th ACM Symposium on Principles of Distributed Computing (PODC 2017). ACM Press, 101--110.

Digital Library

[9]

Yi-Jun Chang, Tsvi Kopelowitz, and Seth Pettie. 2016. An Exponential Separation between Randomized and Deterministic Complexity in the LOCAL Model. In Proc. 57th IEEE Symposium on Foundations of Computer Science (FOCS 2016). IEEE, 615--624.

[10]

Yi-Jun Chang and Seth Pettie. 2019. A Time Hierarchy Theorem for the LOCAL Model. SIAM J. Comput. 48, 1 (2019), 33--69.

Digital Library

[11]

Richard Cole and Uzi Vishkin. 1986. Deterministic coin tossing with applications to optimal parallel list ranking. Information and Control 70, 1 (1986), 32--53.

Digital Library

[12]

Mohsen Ghaffari, Fabian Kuhn, and Yannic Maus. 2017. On the complexity of local distributed graph problems. In Proc. 49th ACM SIGACT Symposium on Theory of Computing (STOC 2017). ACM Press, 784--797.

Digital Library

[13]

Mohsen Ghaffari and Hsin-Hao Su. 2017. Distributed Degree Splitting, Edge Coloring, and Orientations. In Proc. 28th ACM-SIAM Symposium on Discrete Algorithms (SODA 2017). Society for Industrial and Applied Mathematics, 2505--2523.

[14]

Janne H Korhonen and Jukka Suomela. 2018. Towards a complexity theory for the congested clique. In Proc. 30th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA 2018). ACM Press, 163--172.

Digital Library

[15]

Nathan Linial. 1992. Locality in Distributed Graph Algorithms. SIAM J. Comput. 21, 1 (1992), 193--201.

Digital Library

[16]

Moni Naor and Larry Stockmeyer. 1995. What Can be Computed Locally? SIAM J. Comput. 24, 6 (1995), 1259--1277.

Digital Library

[17]

Dennis Olivetti. 2020. Round Eliminator: a tool for automatic speedup simulation. https://github.com/olidennis/round-eliminator

[18]

David Peleg. 2000. Distributed Computing: A Locality-Sensitive Approach. Society for Industrial and Applied Mathematics.

[19]

Will Rosenbaum and Jukka Suomela. 2020. Seeing Far vs. Seeing Wide: Volume Complexity of Local Graph Problems. In Proc. 39th ACM Symposium on Principles of Distributed Computing (PODC 2020). ACM Press.

Digital Library

[20]

Václav Rozhoň and Mohsen Ghaffari. 2020. Polylogarithmic-Time Deterministic Network Decomposition and Distributed Derandomization. In Proc. 52nd Annual ACM Symposium on Theory of Computing (STOC 2020). arXiv:1907.10937 http://arxiv.org/abs/1907.10937

Digital Library

Cited By

Balliu ABrandt SFischer MLatypov RMaus YOlivetti DUitto J(2025)Exponential speedup over locality in MPC with optimal memoryDistributed Computing10.1007/s00446-025-00477-9Online publication date: 26-Feb-2025
https://doi.org/10.1007/s00446-025-00477-9
Brandt SChang YGrebík JGrunau CRozhoň VVidnyánszky Z(2024)ON HOMOMORPHISM GRAPHSForum of Mathematics, Pi10.1017/fmp.2024.812Online publication date: 13-May-2024
https://doi.org/10.1017/fmp.2024.8
Chang YStudený JSuomela J(2023)Distributed graph problems through an automata-theoretic lensTheoretical Computer Science10.1016/j.tcs.2023.113710(113710)Online publication date: Jan-2023
https://doi.org/10.1016/j.tcs.2023.113710
Show More Cited By

Index Terms

Brief Announcement: Classification of Distributed Binary Labeling Problems
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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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.

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: 31 July 2020

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Academy of Finland
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PODC '20

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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 ABrandt SFischer MLatypov RMaus YOlivetti DUitto J(2025)Exponential speedup over locality in MPC with optimal memoryDistributed Computing10.1007/s00446-025-00477-9Online publication date: 26-Feb-2025
https://doi.org/10.1007/s00446-025-00477-9
Brandt SChang YGrebík JGrunau CRozhoň VVidnyánszky Z(2024)ON HOMOMORPHISM GRAPHSForum of Mathematics, Pi10.1017/fmp.2024.812Online publication date: 13-May-2024
https://doi.org/10.1017/fmp.2024.8
Chang YStudený JSuomela J(2023)Distributed graph problems through an automata-theoretic lensTheoretical Computer Science10.1016/j.tcs.2023.113710(113710)Online publication date: Jan-2023
https://doi.org/10.1016/j.tcs.2023.113710
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
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
Bousquet NEsperet LPirot F(2021)Distributed Algorithms for Fractional ColoringStructural Information and Communication Complexity10.1007/978-3-030-79527-6_2(15-30)Online publication date: 20-Jun-2021
https://doi.org/10.1007/978-3-030-79527-6_2
Suomela J(2020)Using Round Elimination to Understand LocalityACM SIGACT News10.1145/3427361.342737451:3(63-81)Online publication date: 29-Sep-2020
https://dl.acm.org/doi/10.1145/3427361.3427374

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