ResearchTrend.AI
  • Papers
  • Communities
  • Events
  • Blog
  • Pricing
Papers
Communities
Social Events
Terms and Conditions
Pricing
Parameter LabParameter LabTwitterGitHubLinkedInBlueskyYoutube

© 2025 ResearchTrend.AI, All rights reserved.

  1. Home
  2. Papers
  3. 2206.00976
49
18

Distributed Edge Coloring in Time Polylogarithmic in ΔΔΔ

2 June 2022
Alkida Balliu
S. Brandt
Fabian Kuhn
Dennis Olivetti
ArXiv (abs)PDFHTML
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)(2\Delta-1)(2Δ−1)-edge coloring can be computed in time polylog⁡Δ+O(log⁡∗n)\mathrm{poly}\log\Delta + O(\log^* n)polylogΔ+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\DeltaΔ. We further show that in the CONGEST model, an (8+ε)Δ(8+\varepsilon)\Delta(8+ε)Δ-edge coloring can be computed in polylog⁡Δ+O(log⁡∗n)\mathrm{poly}\log\Delta + O(\log^* n)polylogΔ+O(log∗n) rounds. The best previous O(Δ)O(\Delta)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)Δ2^{O(1/\varepsilon)}\Delta2O(1/ε)Δ-edge coloring in time O(Δε+log⁡∗n)O(\Delta^\varepsilon + \log^* n)O(Δε+log∗n) for any ε∈(0,1]\varepsilon\in(0,1]ε∈(0,1].

View on arXiv
Comments on this paper