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

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