Optimal Binary Space Partitions in the Plane

  • Mark de Berg
  • Amirali Khosravi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6196)


An optimal bsp for a set S of disjoint line segments in the plane is a bsp for S that produces the minimum number of cuts. We study optimal bsps for three classes of bsps, which differ in the splitting lines that can be used when partitioning a set of fragments in the recursive partitioning process: free bsps can use any splitting line, restricted bsps can only use splitting lines through pairs of fragment endpoints, and auto-partitions can only use splitting lines containing a fragment. We obtain the two following results:

  • It is np-hard to decide whether a given set of segments admits an auto-partition that does not make any cuts.

  • An optimal restricted bsp makes at most 2 times as many cuts as an optimal free bsp for the same set of segments.


Full Version Splitting Line Negative Clause Variable Gadget Planar Instance 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Mark de Berg
    • 1
  • Amirali Khosravi
    • 1
  1. 1.TU EindhovenEindhovenThe Netherlands

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