A Levelset Algorithm for 3D-Tarski

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 $Ω(\log^2 N)$ query lower bound due to Etessami et al. as well as the existing state-of-the-art algorithm due to Fearnley et al.