Discrete & Computational Geometry

, Volume 30, Issue 1, pp 3-16

First online:

A Note on Binary Plane Partitions

  •  TóthAffiliated withDepartment of Computer Science, University of California at Santa Barbara, Santa Barbara, CA 93106, USA toth@cs.ucsb.edu

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Abstract. This paper considers binary space partition s (BSP for short) for disjoint line segments in the plane. The BSP for a disjoint set of objects is a scheme dividing the space recursively by hyperplanes until the resulting fragments of objects are separated. The size of a BSP is the number of resulting fragments of the objects. We show that the minimal size of a BSP for n disjoint line segments in the plane is Ω (n log n /log log n) in the worst case.