Distributed Edge Coloring and a Special Case of the Constructive Lovász Local Lemma

@article{Chang2020DistributedEC,
  title={Distributed Edge Coloring and a Special Case of the Constructive Lov{\'a}sz Local Lemma},
  author={Yi-Jun Chang and Qizheng He and Wenzheng Li and Seth Pettie and Jara Uitto},
  journal={ACM Transactions on Algorithms (TALG)},
  year={2020},
  volume={16},
  pages={1 - 51}
}
The complexity of distributed edge coloring depends heavily on the palette size as a function of the maximum degree Δ. In this article, we explore the complexity of edge coloring in the LOCAL model in different palette size regimes. Our results are as follows. Lower Bounds: First, we simplify the round elimination technique of Brandt et al. [16] and prove that (2Δ −2)-edge coloring requires Ω (logΔ log n) time with high probability and Ω (logΔ n) time deterministically, even on trees. Second… 

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