We give a new randomized distributed algorithm for the $\Delta+1$-list coloring problem. The algorithm and its analysis dramatically simplify the previous best result known of Chang, Li, and Pettie [SICOMP 2020]. This allows for numerous refinements, and in particular, we can color all $n$-node graphs of maximum degree $\Delta \ge \log^{2+\Omega(1)} n$ in $O(\log^* n)$ rounds. The algorithm works in the CONGEST model, i.e., it uses only $O(\log n)$ bits per message for communication. On low-degree graphs, the algorithm shatters the graph into components of size $\operatorname{poly}(\log n)$ in $O(\log^* \Delta)$ rounds, showing that the randomized complexity of $\Delta+1$-list coloring in CONGEST depends inherently on the deterministic complexity of related coloring problems.
翻译：我们为$Delta+1$列表的彩色问题提供了一个新的随机分布算法。 算法及其分析极大地简化了先前已知的张、 李和佩蒂[SICOMP 2020] 的最佳结果。 这可以进行许多改进, 特别是, 我们可以用$O( log)\\\ ge\ log\\\ ⁇ 2\\\ \\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 美元来显示最大度的彩色色的无序复杂性。 。 在 CONEST 模型中,, 它只使用$O( \ \ n) 每条信息只使用$O\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
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