Discrete & Computational Geometry

, Volume 30, Issue 1, pp 3–16

A Note on Binary Plane Partitions

DOI: 10.1007/s00454-003-2921-x

Cite this article as:
Tóth Discrete Comput Geom (2003) 30: 3. doi:10.1007/s00454-003-2921-x

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.

Copyright information

© 2003 Springer-Verlag New York Inc.

Authors and Affiliations

  •  Tóth
    • 1
  1. 1.Department of Computer Science, University of California at Santa Barbara, Santa Barbara, CA 93106, USA toth@cs.ucsb.eduUS