Discrete & Computational Geometry

, Volume 45, Issue 4, pp 617–646 | Cite as

Binary Plane Partitions for Disjoint Line Segments

  • Csaba D. Tóth


A binary space partition (BSP) for a set of disjoint objects in Euclidean space is a recursive decomposition where each step partitions the space (and possibly some of the objects) along a hyperplane and recurses on the objects clipped in each of the two open half-spaces. The size of a BSP is defined as the number of resulting fragments of the input objects. It is shown that every set of n disjoint line segments in the plane admits a BSP of size O(nlog n/log log n). This bound is the best possible.


Binary space partitions Line segments 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada

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