Binary space partitions for axis-paralles line segments: size-height tradeoffs

Authors:
Sunil Arya
Affiliations:
Department of Computer Science, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Venue:
Information Processing Letters
Year:
2002

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Abstract

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 Ω (n log n) and a BSP tree of size O(n) must have height Ω(nδ), where δ is a suitable constant.