Binary space partitions of orthogonal subdivisions

We consider the problem of constructing binary space partitions (BSPs) for orthogonal subdivisions (space filling packings of boxes) in d-space. We show that a subdivision with n boxes can be refined into a BSP of size O(n d+1 3 ), for all d ≥ 3, and that such a partition can be computed in time O(K log n), where K is the size of the BSP produced. Our upper bound on the BSP size is tight for 3-dimensional subdivisions; in higher dimensions, this is the first nontrivial result for general full-dimensional boxes. We also present a lower bound construction for a subdivision of n boxes in d-space for which every axis-aligned BSP has Ω(nβ(d) ) size, where β(d) converges to (1 + √ 5)/2 as d → ∞.

• Type: Conference
• Year: 2004
• Where: COMPGEOM
• Authors: John Hershberger, Subhash Suri, Csaba D. Tóth
• Keywords: Binary Space Partitions, BSP Size, COMPGEOM 2004, Space filling Packings