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Binary Space Partitions

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  • First Online:
Encyclopedia of Algorithms

Years and Authors of Summarized Original Work

  • 1990; Paterson, Yao

  • 1992; D’Amore, Franciosa

  • 1992; Paterson, Yao

  • 2002; Berman, DasGupta, Muthukrishnan

  • 2003; Tóth

  • 2004; Dumitrescu, Mitchell, Sharir

  • 2005; Hershberger, Suri, Tóth

  • 2011; Tóth

Binary Space Partitions, Fig. 1
figure 25 figure 25

Three 2-dimensional convex objects and a line segment (left), a binary space partition with five partition lines \(H_{1},\ldots ,H_{5}\) (center), and the corresponding BSP tree (right)

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Recommended Reading

  1. d’Amore F, Franciosa PG (1992) On the optimal binary plane partition for sets of isothetic rectangles. Inf Process Lett 44:255–259

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  2. Basch J, Guibas LJ, Hershberger J (1999) Data structures for mobile data. J Algorithms 31(1):1–28

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  6. 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):252–267

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  7. Dumitrescu A, Mitchell JSB, Sharir M (2004) Binary space partitions for axis-parallel segments, rectangles, and hyperrectangles. Discret Comput Geom 31(2):207–227

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  8. 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 100–108

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  9. Hershberger J, Suri S, Tóth CsD (2005) Binary space partitions of orthogonal subdivisions. SIAM J Comput 34(6):1380–1397

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  10. Paterson MS, Yao FF (1990) Efficient binary space partitions for hidden-surface removal and solid modeling. Discret Comput Geom 5:485–503

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  11. Paterson MS, Yao FF (1992) Optimal binary space partitions for orthogonal objects. J Algorithms 13:99–113

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  12. Tóth CsD (2003) A note on binary plane partitions. Discret Comput Geom 30:3–16

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  13. 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 529–556

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  14. Tóth CsD (2008) Binary space partition for axis-aligned fat rectangles. SIAM J Comput 38(1):429–447

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  15. Tóth CsD (2011) Binary plane partitions for disjoint line segments. Discret Comput Geom 45(4):617–646

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Author information

Authors and Affiliations

  1. Computer Science, University of Wisconsin–Milwaukee, Milwaukee, WI, USA

    Adrian Dumitrescu

  2. Department of Computer Science, Tufts University, Medford, MA, USA

    Csaba D. Tóth

  3. Department of Mathematics, California State University Northridge, 18111 Nordhoff St, 91330, Los Angeles, CA, USA

    Csaba D. Tóth

Authors
  1. Adrian Dumitrescu
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  2. Csaba D. Tóth
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Corresponding author

Correspondence to Adrian Dumitrescu .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Dumitrescu, A., Tóth, C.D. (2016). Binary Space Partitions. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_511

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