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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)

Abstract

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.

Keywords

Full Version Splitting Line Negative Clause Variable Gadget Planar Instance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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