Binary space partitions for axis-parallel line segments: Size-height tradeoffs

We present worst-case lower bounds on the minimum size of a binary space partition (BSP) tree as a function of its height, for a set S of n axis-parallel line segments in the plane. We assume that the BSP uses only axis-parallel cutting lines. These lower bounds imply that, in the worst case, a BSP tree of height O(log n) must have size (n log n) and a BSP tree of size O(n) must have height (n ), where is a suitable constant. Key words: Computational geometry, binary space partitions, line segments.

• Type: Journal
• Year: 2002
• Where: IPL
• Authors: Sunil Arya
• Keywords: Binary Space Partitions, IPL 2002, Lower Bounds, Worst-case Lower Bounds