Definition
Plain language
Finding which points in a collection lie on a given side of a line or plane.
As stated in the literature
A classical computational-geometry problem: given a set of points and a query halfspace, retrieve all points contained in it, with various data structures providing tradeoffs.
Why it matters: It underlies many spatial-query systems and is a classical proving ground for designing data structures with sharp performance tradeoffs.
For example, given a million city locations, find all the ones west of a given line on the map as fast as possible.
Heard on the show
“It's called halfspace range searching.”Episode 036 — Sparse Attention Was the Wrong Frame. Treat It as Geometry Instead.