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 $O(\log \Delta) + 2^{O(\sqrt{\log\log n})}$. 
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