We show that any algorithm that solves the sinkless orientation problem in the supported LOCAL model requires $\Omega(\log n)$ rounds, and this is tight. The supported LOCAL is at least as strong as the usual LOCAL model, and as a corollary this also gives a new, short and elementary proof that shows that the round complexity of the sinkless orientation problem in the deterministic LOCAL model is $\Omega(\log n)$.
翻译:我们显示,任何解决支持的 LOCAL 模型中无沉没方向问题的算法都需要$\ Omega (\log n) 圆($\ log n) 圆圆,而且这个回合很紧。 得到支持的 LOCAL 至少和通常的 LOCOL 模型一样强大, 作为推论,这也提供了一个新的、简短和基本的证据,表明确定性的 LOCAL 模型中无沉没方向问题的轮复杂程度是$\ Omega (\log n) 。