We present a simple new algorithm for finding a Tarski fixed point of a monotone function $F : [N]^3 \rightarrow [N]^3$. Our algorithm runs in $O(\log^2 N)$ time and makes $O(\log^2 N)$ queries to $F$, matching the $\Omega(\log^2 N)$ query lower bound due to Etessami et al.\ as well as the existing state-of-the-art algorithm due to Fearnley et al.

翻译：我们提出了一种新的简单算法，用于寻找单调函数 $F : [N]^3 \rightarrow [N]^3$ 的塔尔斯基不动点。我们的算法运行时间为 $O(\log^2 N)$，并对 $F$ 进行 $O(\log^2 N)$ 次查询，这与 Etessami 等人证明的 $\Omega(\log^2 N)$ 查询下界以及 Fearnley 等人提出的现有最先进算法的复杂度相匹配。