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Distributed (Δ +1)-Coloring in Sublogarithmic Rounds

Authors:

David G. Harris,

Johannes Schneider,

Hsin-Hao SuAuthors Info & Claims

Journal of the ACM (JACM), Volume 65, Issue 4

Article No.: 19, Pages 1 - 21

https://doi.org/10.1145/3178120

Published: 12 April 2018 Publication History

Abstract

We give a new randomized distributed algorithm for (Δ +1)-coloring in the LOCAL model, running in O(√ log Δ)+ 2^{O(√log log n}) rounds in a graph of maximum degree Δ. This implies that the (Δ +1)-coloring problem is easier than the maximal independent set problem and the maximal matching problem, due to their lower bounds of Ω(min(√/log n log log n, /log Δ log log Δ)) by Kuhn, Moscibroda, and Wattenhofer [PODC’04]. Our algorithm also extends to list-coloring where the palette of each node contains Δ +1 colors. We extend the set of distributed symmetry-breaking techniques by performing a decomposition of graphs into dense and sparse parts.

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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
Flin MGhaffari MHalldórsson MKuhn FNolin AAgrawal KShun J(2023)Coloring Fast with BroadcastsProceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3558481.3591095(455-465)Online publication date: 17-Jun-2023
https://dl.acm.org/doi/10.1145/3558481.3591095
Halldórsson MNolin A(2023)Superfast coloring in CONGEST via efficient color samplingTheoretical Computer Science10.1016/j.tcs.2023.113711948:COnline publication date: 28-Feb-2023
https://dl.acm.org/doi/10.1016/j.tcs.2023.113711
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Index Terms

Distributed (Δ +1)-Coloring in Sublogarithmic Rounds
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms

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Published In

cover image Journal of the ACM

Journal of the ACM Volume 65, Issue 4

Distributed Computing, Cryptography, Distributed Computing, Cryptography, Coding Theory, Automata Theory, Complexity Theory, Programming Languages, Algorithms, Invited Paper Foreword and Databases

August 2018

307 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/3208081

Editor:
Éva Tardos
Cornell University

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Copyright © 2018 ACM.

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Publication History

Published: 12 April 2018

Accepted: 01 January 2018

Revised: 01 November 2017

Received: 01 June 2016

Published in JACM Volume 65, Issue 4

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Cited By

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
Flin MGhaffari MHalldórsson MKuhn FNolin AAgrawal KShun J(2023)Coloring Fast with BroadcastsProceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3558481.3591095(455-465)Online publication date: 17-Jun-2023
https://dl.acm.org/doi/10.1145/3558481.3591095
Halldórsson MNolin A(2023)Superfast coloring in CONGEST via efficient color samplingTheoretical Computer Science10.1016/j.tcs.2023.113711948:COnline publication date: 28-Feb-2023
https://dl.acm.org/doi/10.1016/j.tcs.2023.113711
Halldórsson MKuhn FNolin ATonoyan TLeonardi SGupta A(2022)Near-optimal distributed degree+1 coloringProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3520023(450-463)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519935.3520023
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
Halldórsson MNolin ATonoyan TMilani AWoelfel P(2022)Overcoming Congestion in Distributed ColoringProceedings of the 2022 ACM Symposium on Principles of Distributed Computing10.1145/3519270.3538438(26-36)Online publication date: 20-Jul-2022
https://dl.acm.org/doi/10.1145/3519270.3538438
Maus YTonoyan T(2022)Linial for listsDistributed Computing10.1007/s00446-022-00424-y35:6(533-546)Online publication date: 1-Dec-2022
https://dl.acm.org/doi/10.1007/s00446-022-00424-y
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
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Halldórsson MKuhn FMaus YTonoyan TKhuller SVassilevska Williams V(2021)Efficient randomized distributed coloring in CONGESTProceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing10.1145/3406325.3451089(1180-1193)Online publication date: 15-Jun-2021
https://dl.acm.org/doi/10.1145/3406325.3451089
Chang YLi WPettie S(2020)Distributed $(\Delta+1)$-Coloring via Ultrafast Graph ShatteringSIAM Journal on Computing10.1137/19M124952749:3(497-539)Online publication date: 19-May-2020
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