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Optimal Binary Space Partitions in the Plane

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Book cover Computing and Combinatorics (COCOON 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6196))

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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.

This research was supported by the Netherlands’ Organisation for Scientific Research (NWO) under project no. 639.023.301.

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Author information

Authors and Affiliations

  1. TU Eindhoven, P.O. Box 513, 5600, MB, Eindhoven, The Netherlands

    Mark de Berg & Amirali Khosravi

Authors
  1. Mark de Berg
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  2. Amirali Khosravi
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Editor information

Editors and Affiliations

  1. University of Florida, CSE Building, Room 566, P.O. Box 116120, 32611-6120, Gainesville, Florida, USA

    My T. Thai

  2. Department of Computer and Information Science and Technology, University of Florida, P.O. Box, USA

    Sartaj Sahni

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de Berg, M., Khosravi, A. (2010). Optimal Binary Space Partitions in the Plane. In: Thai, M.T., Sahni, S. (eds) Computing and Combinatorics. COCOON 2010. Lecture Notes in Computer Science, vol 6196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14031-0_25

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  • DOI: https://doi.org/10.1007/978-3-642-14031-0_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14030-3

  • Online ISBN: 978-3-642-14031-0

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