We give practical, efficient algorithms that automatically determine the asymptotic distributed round complexity of a given locally checkable graph problem in the $[\Theta(\log n), \Theta(n)]$ region, in two settings. We present one algorithm for unrooted regular trees and another algorithm for rooted regular trees. The algorithms take the description of a locally checkable labeling problem as input, and the running time is polynomial in the size of the problem description. The algorithms decide if the problem is solvable in $O(\log n)$ rounds. If not, it is known that the complexity has to be $\Theta(n^{1/k})$ for some $k = 1, 2, \dotsc$, and in this case the algorithms also output the right value of the exponent $k$. In rooted trees in the $O(\log n)$ case we can then further determine the exact complexity class by using algorithms from prior work; for unrooted trees the more fine-grained classification in the $O(\log n)$ region remains an open question.

翻译：在 $[Theta(\log n),\ Theta(n)] $(n)] 区域中,我们给出实际有效的算法,在两个设置中自动确定特定本地可检查的图表问题无症状分布的圆形复杂度。我们为未扎根的普通树提供了一种算法,为已扎根的普通树提供了另一种算法。这些算法将本地可核实的标签问题描述为输入,运行时间是问题描述大小的多元性。这些算法决定了问题是否在$O(\log n) 回合中可以溶解。如果不是,我们知道问题的复杂性必须是$(theta) = 1, 2,\dotsc$(n) 美元,而在这种情况下,算法也输出了Exponent $(\log n) 的正确值。在$O (\log n) 案例中的根树,我们随后可以通过使用先前工作的算法进一步确定确切的复杂程度;对于未扎根的树木,在$O(n) $(\log n) 区域中更精确的分类仍然是个未决问题。