Box Sort, a multidimensional binary sorting method for rectangular boxes, used for quick range searching (original) (raw)

Abstract

In many geometrical applications data needs to be sorted in more than one dimension to speed up running time. For example, the evaluation of set operations on polygons, and hidden-surface algorithms. We describe an efficient algorithm for doing this, which we call “Box Sort”. Given are_N_ boxes in a_n_-dimensional space. A box is a spatial region bounded by (hyper-)planes orthogonal to the coordinate axes. Box Sort is a multidimensional sorting method for the_N_ boxes, which allows us to perform quick range queries (“box searches”) with respect to these boxes. When the given_N_ boxes are sufficiently scattered around the_n_-dimensional space, the box search for an arbitrary query box of the same order of size as the sorted boxes can be carried out in_O_(log_N_) time. The necessary memory requirement for Box Sort is invariably_O(N)_.

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References

• Bentley J (1975) Multidimensional Binary Search Trees Used for Associated Searching. Commun ACM 18(9):509–517
  Article Google Scholar
• Bentley J, Friedman J (1979) Data Structures for Range Searching. Comput Surv 11(4):397–409
  Article Google Scholar
• Rosenberg J (1985) Geographical Data Structures Compared: A Study of Data Structures Supporting Region Queries. IEEE Trans CAD Integrated Circuits Syst 4(1):53–67
  Article Google Scholar
• Samet H (1984) The Quadtree and Related Hierarchical Data Structures. Comput Surv 16(2):187–260
  Article MathSciNet Google Scholar
• Sutherland I, Sproull R, Schumaker R (1974) A Characterization of Ten Hidden-Surface Algorithms. Comput Surv 6(1):1–55
  Article Google Scholar
• Wirth N (1976) Algorithms+data+structures=programs. Prentice-Hall, Englewood Cliffs, NJ
  Google Scholar

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Authors and Affiliations

1. D.I.S.C. (Digitized Information Systems Corporation), Nieuwevaart 153, B-9000, Gent, Belgium
   Piet Houthuys

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1. Piet Houthuys
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Houthuys, P. Box Sort, a multidimensional binary sorting method for rectangular boxes, used for quick range searching.The Visual Computer 3, 236–249 (1987). https://doi.org/10.1007/BF01952830

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• Issue Date: December 1987
• DOI: https://doi.org/10.1007/BF01952830

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