research-article

Efficient Deterministic Distributed Coloring with Small Bandwidth

Authors:

Philipp Bamberger,

Yannic MausAuthors Info & Claims

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

Pages 243 - 252

https://doi.org/10.1145/3382734.3404504

Published: 31 July 2020 Publication History

Abstract

We show that the (degree + 1)-list coloring problem can be solved deterministically in O(D · log n · log² Δ) rounds in the CONGEST model, where D is the diameter of the graph, n the number of nodes, and Δ the maximum degree. Using the recent polylogarithmic-time deterministic network decomposition algorithm by Rozhoň and Ghaffari [49], this implies the first efficient (i.e., poly log n-time) deterministic CONGEST algorithm for the (Δ + 1)-coloring and the (degree + 1)-list coloring problem. Previously the best known algorithm required [EQUATION] rounds and was not based on network decompositions.

Our techniques also lead to deterministic (degree + 1)-list coloring algorithms for the congested clique and the massively parallel computation (MPC) model. For the congested clique, we obtain an algorithm with time complexity O(log Δ · log log Δ), for the MPC model, we obtain algorithms with round complexity O(log² Δ) for the linear-memory regime and O(log² Δ + log n) for the sublinear memory regime.

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Cited By

Coy SCzumaj ADavies-Peck PMishra G(2024)Parallel Derandomization for Coloring*2024 IEEE International Parallel and Distributed Processing Symposium (IPDPS)10.1109/IPDPS57955.2024.00098(1058-1069)Online publication date: 27-May-2024
https://doi.org/10.1109/IPDPS57955.2024.00098
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
Assadi SChakrabarti AGhosh PStoeckl MGeerts FNgo HSintos S(2023)Coloring in Graph Streams via Deterministic and Adversarially Robust AlgorithmsProceedings of the 42nd ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3584372.3588681(141-153)Online publication date: 18-Jun-2023
https://dl.acm.org/doi/10.1145/3584372.3588681
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Index Terms

Efficient Deterministic Distributed Coloring with Small Bandwidth
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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Overall Acceptance Rate 740 of 2,477 submissions, 30%

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Cited By

Coy SCzumaj ADavies-Peck PMishra G(2024)Parallel Derandomization for Coloring*2024 IEEE International Parallel and Distributed Processing Symposium (IPDPS)10.1109/IPDPS57955.2024.00098(1058-1069)Online publication date: 27-May-2024
https://doi.org/10.1109/IPDPS57955.2024.00098
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
Assadi SChakrabarti AGhosh PStoeckl MGeerts FNgo HSintos S(2023)Coloring in Graph Streams via Deterministic and Adversarially Robust AlgorithmsProceedings of the 42nd ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3584372.3588681(141-153)Online publication date: 18-Jun-2023
https://dl.acm.org/doi/10.1145/3584372.3588681
Maus YPeltonen SUitto JOshman RNolin AHalldorsson MBalliu A(2023)Distributed Symmetry Breaking on Power Graphs via SparsificationProceedings of the 2023 ACM Symposium on Principles of Distributed Computing10.1145/3583668.3594579(157-167)Online publication date: 19-Jun-2023
https://dl.acm.org/doi/10.1145/3583668.3594579
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
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Fischer MGiliberti JGrunau CAgrawal KShun J(2023)Deterministic Massively Parallel Symmetry Breaking for Sparse GraphsProceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3558481.3591081(89-100)Online publication date: 17-Jun-2023
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Coy SCzumaj ALeonardi SGupta A(2022)Deterministic massively parallel connectivityProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3520055(162-175)Online publication date: 9-Jun-2022
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Ghaffari MKuhn F(2022)Deterministic Distributed Vertex Coloring: Simpler, Faster, and without Network Decomposition2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS52979.2021.00101(1009-1020)Online publication date: Feb-2022
https://doi.org/10.1109/FOCS52979.2021.00101
Maus YTonoyan T(2022)Linial for listsDistributed Computing10.1007/s00446-022-00424-y35:6(533-546)Online publication date: 17-May-2022
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Ghaffari MGrunau CRozhoň VMarx D(2021)Improved deterministic network decompositionProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458237(2904-2923)Online publication date: 10-Jan-2021
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