## Binary Plane Partitions for Disjoint Line Segments

by
Csaba D. Tóth

Citations: | 1 - 1 self |

### BibTeX

@MISC{Tóth_binaryplane,

author = {Csaba D. Tóth},

title = {Binary Plane Partitions for Disjoint Line Segments},

year = {}

}

### OpenURL

### Abstract

A binary space partition (BSP) for a set of disjoint objects in Euclidean space is a recursive decomposition, where each step partitions the space (and some of the objects) along a hyperplane and recurses on the objects clipped in each of the two open halfspaces. The size of a BSP is defined as the number of resulting fragments of the input objects. It is shown that every set of n disjoint line segments in the plane admits a BSP of size O(n log n / log log n). This bound is best possible apart from the constant factor. 1