# Coloring Fast Without Learning Your Neighbors' Colors

@article{Halldrsson2020ColoringFW,
title={Coloring Fast Without Learning Your Neighbors' Colors},
author={M. Halld{\'o}rsson and F. Kuhn and Yannic Maus and Alexandre Nolin},
journal={ArXiv},
year={2020},
volume={abs/2008.04303}
}
We give an improved randomized CONGEST algorithm for distance-$2$ coloring that uses $\Delta^2+1$ colors and runs in $O(\log n)$ rounds, improving the recent $O(\log \Delta \cdot \log n)$-round algorithm in [Halldorsson, Kuhn, Maus; PODC '20]. We then improve the time complexity to $O(\log \Delta) + 2^{O(\sqrt{\log\log n})}$.
3 Citations
Efficient CONGEST Algorithms for the Lovasz Local Lemma
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• ArXiv
• 2021
A poly log log n time randomized CONGEST algorithm for a natural class of Lovász Local Lemma (LLL) instances on constant degree graphs implies that there are no LCL problems with randomized complexity between log n and poly loglog n. Expand
Efficient randomized distributed coloring in CONGEST
• Mathematics, Computer Science
• STOC
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This work presents a new randomized distributed vertex coloring algorithm for the standard CONGEST model, where the network is modeled as an n-node graph G, and where the nodes of G operate in synchronous communication rounds in which they can exchange O(logn)-bit messages over all the edges of G. Expand
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An O(log∗ ∆)-round CONGEST algorithm for (2∆− 1)-edge coloring when ∆ ≥ log n, and poly(log logn)-round algorithm in general is obtained. Expand

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