We introduce a new type of partition called a parallel planes partition. We prove there exists a parallel planes partition of any set of n points in arbitrary dimension. This partition yields a data structure for the half-space retrieval problem in arbitrary dimension; it has linear size and achieves a sublinear query time. Also, we give efficient algorithms for computing this partition. © 1987.
Cole, R. (1987). Partitioning point sets in arbitrary dimension. Theoretical Computer Science, 49(2–3), 239–265. https://doi.org/10.1016/0304-3975(87)90009-0