Encyclopedia of Algorithms

Living Edition
| Editors: Ming-Yang Kao

Binary Space Partitions

  • Adrian Dumitrescu
  • Csaba D. Tóth
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27848-8_511-1

Years and Authors of Summarized Original Work

1990; Paterson, Yao

1992; Paterson, Yao

1992; D’Amore, Franciosa

2002; Berman, DasGupta, Muthukrishnan

2003; Tóth

2004; Dumitrescu, Mitchell, Sharir

2005; Hershberger, Suri, Tóth

2011; Tóth

Problem Definition

The binary space partition (for short, BSP) is a scheme for subdividing the ambient space \(\mathbb{R}^{d}\)


Computational geometry Recursive partition Convex decomposition BSP tree 
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Recommended Reading

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    d’Amore F, Franciosa PG (1992) On the optimal binary plane partition for sets of isothetic rectangles. Inf Process Lett 44:255–259MathSciNetCrossRefzbMATHGoogle Scholar
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    Basch J, Guibas LJ, Hershberger J (1999) Data structures for mobile data. J Algorithms 31(1):1–28MathSciNetCrossRefzbMATHGoogle Scholar
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    de Berg M, Cheong O, van Kreveld M, Overmars M (2008) Computational geometry, 3rd edn. Springer, BerlinCrossRefzbMATHGoogle Scholar
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    de Berg M, de Groot M, Overmars MH (1997) Perfect binary space partitions. Comput Geom Theory Appl 7:81–91CrossRefzbMATHGoogle Scholar
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    Berman P, DasGupta B, Muthukrishnan S (2002) On the exact size of the binary space partitioning of sets of isothetic rectangles with applications. SIAM J Discret Math 15(2):252–267MathSciNetCrossRefzbMATHGoogle Scholar
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    Dumitrescu A, Mitchell JSB, Sharir M (2004) Binary space partitions for axis-parallel segments, rectangles, and hyperrectangles. Discret Comput Geom 31(2):207–227MathSciNetCrossRefzbMATHGoogle Scholar
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    Hershberger J, Suri S (2003) Binary space partitions for 3D subdivisions. In: Proceedings of the 14th ACM-SIAM symposium on discrete algorithms, Baltimore. ACM, pp 100–108Google Scholar
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    Hershberger J, Suri S, Tóth CsD (2005) Binary space partitions of orthogonal subdivisions. SIAM J Comput 34(6):1380–1397MathSciNetCrossRefzbMATHGoogle Scholar
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    Paterson MS, Yao FF (1990) Efficient binary space partitions for hidden-surface removal and solid modeling. Discret Comput Geom 5:485–503MathSciNetCrossRefzbMATHGoogle Scholar
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    Paterson MS, Yao FF (1992) Optimal binary space partitions for orthogonal objects. J Algorithms 13:99–113MathSciNetCrossRefzbMATHGoogle Scholar
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    Tóth CsD (2003) A note on binary plane partitions. Discret Comput Geom 30:3–16CrossRefzbMATHGoogle Scholar
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    Tóth CsD (2005) Binary space partitions: recent developments. In: Goodman JE, Pach J, Welzl E (eds) Combinatorial and Computational Geometry. Volume 52 of MSRI Publications, Cambridge University Press, Cambridge, pp 529–556Google Scholar
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    Tóth CsD (2008) Binary space partition for axis-aligned fat rectangles. SIAM J Comput 38(1):429–447MathSciNetCrossRefzbMATHGoogle Scholar
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    Tóth CsD (2011) Binary plane partitions for disjoint line segments. Discret Comput Geom 45(4):617–646CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Computer Science, University of Wisconsin–MilwaukeeMilwaukee, WIUSA
  2. 2.Department of Mathematics, California State University NorthridgeLos Angeles, CAUSA
  3. 3.Department of Computer Science, Tufts UniversityMedford, MAUSA