4 research outputs found
Kinetic kd-Trees and Longest-Side kd-Trees
We propose a simple variant of kd-trees, called rank-based kd-trees, for sets of points in~.
We show that a rank-based kd-tree, like an ordinary kd-tree, supports range search que-ries in~ time,
where~ is the output size. The main advantage of rank-based kd-trees is that they can be efficiently kinetized:
the KDS processes~ events in the worst case, assuming that the points follow constant-degree algebraic trajectories,
each event can be handled in~ time, and each point is involved in~ 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~. 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~ time.
The KDS processes~ events in the worst case, assuming that the points follow constant-degree algebraic trajectories;
each event can be handled in~ time, and each point is involved in~ certificates