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Distributed Edge Coloring in Time Polylogarithmic in Δ

Authors:

Sebastian Brandt,

Dennis OlivettiAuthors Info & Claims

PODC'22: Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing

Pages 15 - 25

https://doi.org/10.1145/3519270.3538440

Published: 21 July 2022 Publication History

Abstract

We provide new deterministic algorithms for the edge coloring problem, which is one of the classic and highly studied distributed local symmetry breaking problems. As our main result, we show that a (2Δ - 1)-edge coloring can be computed in time poly log Δ + O(log* n) in the LOCAL model. This improves a result of Balliu, Kuhn, and Olivetti [PODC '20], who gave an algorithm with a quasi-polylogarithmic dependency on Δ. We further show that in the CONGEST model, an (8 + ε)Δ-edge coloring can be computed in poly log Δ + O(log* n) rounds. The best previous O(Δ)-edge coloring algorithm that can be implemented in the CONGEST model is by Barenboim and Elkin [PODC '11] and it computes a 2O(1/ε)Δ- edge coloring in time O(Δε + log* n) for any ε ∈ (0, 1].

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Cited By

Bhattacharya SCarmon DCosta MSolomon SZhang T(2024)Faster $(\Delta+1)$-Edge Coloring: Breaking the $m\sqrt{n}$ Time Barrier2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS61266.2024.00128(2186-2201)Online publication date: 27-Oct-2024
https://doi.org/10.1109/FOCS61266.2024.00128
Maus Y(2023)Distributed Graph Coloring Made EasyACM Transactions on Parallel Computing10.1145/360589610:4(1-21)Online publication date: 14-Dec-2023
https://dl.acm.org/doi/10.1145/3605896

Index Terms

Distributed Edge Coloring in Time Polylogarithmic in Δ
1. Theory of computation
  1. Design and analysis of algorithms
    1. Distributed algorithms

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cover image ACM Conferences

PODC'22: Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing

July 2022

509 pages

ISBN:9781450392624

DOI:10.1145/3519270

General Chair:
Alessia Milani
Aix-Marseille University, France
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Program Chair:
Philipp Woelfel
University of Calgary, Canada

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Published: 21 July 2022

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Cited By

Bhattacharya SCarmon DCosta MSolomon SZhang T(2024)Faster $(\Delta+1)$-Edge Coloring: Breaking the $m\sqrt{n}$ Time Barrier2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS61266.2024.00128(2186-2201)Online publication date: 27-Oct-2024
https://doi.org/10.1109/FOCS61266.2024.00128
Maus Y(2023)Distributed Graph Coloring Made EasyACM Transactions on Parallel Computing10.1145/360589610:4(1-21)Online publication date: 14-Dec-2023
https://dl.acm.org/doi/10.1145/3605896

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