Binary plane partitions for disjoint line segments

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.

• Type: Conference
• Year: 2009
• Where: COMPGEOM
• Authors: Csaba D. Tóth
• Keywords: Binary Space Partition, COMPGEOM 2009, Discrete Geometry, Disjoint Line Segments, Disjoint Objects