We propose a simple variant of kd-trees, called rank-based kd-trees, for sets of points in~$Reals^d$.

We show that a rank-based kd-tree, like an ordinary kd-tree, supports range search que-ries in~$O(n^{1-1/d}+k)$ time,

where~$k$ is the output size. The main advantage of rank-based kd-trees is that they can be efficiently kinetized:

the KDS processes~$O(n^2)$ events in the worst case, assuming that the points follow constant-degree algebraic trajectories,

each event can be handled in~$O(log n)$ time, and each point is involved in~$O(1)$ certificates.

We also propose a variant of longest-side kd-trees, called rank-based longest-side kd-trees (RBLS kd-trees, for short),

for sets of points in~$Reals^2$. RBLS kd-trees can be kinetized efficiently as well and like longest-side kd-trees,

RBLS kd-trees support nearest-neighbor, farthest-neighbor, and approximate range search queries in~$O((1/epsilon)log^2 n)$ time.

The KDS processes~$O(n^3log n)$ events in the worst case, assuming that the points follow constant-degree algebraic trajectories;

each event can be handled in~$O(log^2 n)$ time, and each point is involved in~$O(log n)$ certificates.