A paging scheme for pointer-based quadtrees

  • Clifford A. Shaffer
  • Patrick R. Brown
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 692)


Hierarchical data structures, most notably the quadtree, have become increasingly popular for the indexing of the large databases required by GIS since they support the efficient computation of traditional GIS spatial analysis algorithms. While the quadtree has many representations, the linear quadtree has become the standard. Initially thought to be more space efficient than traditional pointer-based quadtree representations, its main operational virtue has been its ability to minimize data transfers between main memory and disk. Recent results show that a good pointer-based representation is more space efficient than the linear quadtree. This paper presents a pointer-based representation for quadtrees called the paged-pointer quadtree, which partitions the nodes of a pointer-based quadtree into pages and manages the pages using B-tree techniques. A paged-pointer quadtree always requires less space than the corresponding linear quadtree. Our initial implementation provides better performance than a highly optimized system based on linear quadtrees.


Leaf Node Internal Node Parent Pointer Locational Code Page Fault 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Abe84]
    D.J. Abel. A B+-tree structure for large quadtrees. Computer Vision, Graphics, and Image Processing, 27:19–31, July 1984.Google Scholar
  2. [BFGS86]
    L. Bergman, H. Fuchs, E. Grant and S. Spach. Image rendering by adaptive refinement, Computer Graphics, 20(4):29–37, August 1986.Google Scholar
  3. [Brown92]
    P.R. Brown. A paging scheme for pointer-based quadtrees. Masters Thesis, Virginia Tech, Blacksburg VA, May 1992.Google Scholar
  4. [DT81]
    L.J. Doctor and J.G. Torborg. Display techniques for octree-encoded objects. IEEE Computer Graphics & Applications, 1(3): 29–38, July 1981.Google Scholar
  5. [Gar82]
    I. Gargantini. An effective way to represent quadtrees. Communications of the ACM, 25(12):905–910, December 1982.Google Scholar
  6. [HS79]
    G.M. Hunter and K. Steiglitz. Operations on images using quad trees. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1(2):145–153, July 1979.Google Scholar
  7. [JSS91]
    W. de Jonge, P. Scheuermann and A. Schijf. Encoding and manipulating pictorial data with S+-trees, in Advances in Spatial Databases: Proceedings of SSD'91, Lecture Notes in Computer Science 525, O. Günther and H-J. Schek, eds., Springer Verlag, Berlin, 401–419, 1991.Google Scholar
  8. [KE80]
    E. Kawaguchi and T. Endo. On a method of binary picture representation and its application to data compression, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2(1):27–35, January 1980.Google Scholar
  9. [Mor66]
    G.M. Morton. A computer oriented geodetic data base and a new technique in file sequencing. Technical report, IBM, Ottowa, Canada, 1966.Google Scholar
  10. [OHS90]
    D.N. Oskard, T.H. Hong, and C.A. Shaffer. Real-time algorithms and data structures for underwater mapping. IEEE Transactions on Systems, Man, and Cybernetics, 20(6):1469–1475, November 1990.Google Scholar
  11. [Sam90a]
    H. Samet. Applications of Spatial Data Structures: Computer Graphics, Image Processing, and GIS. Addison-Wesley, 1990.Google Scholar
  12. [Sam90b]
    H. Samet. The Design and Analysis of Spatial Data Structures. Addison-Wesley, 1990.Google Scholar
  13. [SS87]
    C.A. Shaffer and H. Samet. Optimal quadtree construction algorithms. Computer Vision, Graphics, and Image Processing, 37:402–419, March 1987.Google Scholar
  14. [SS90]
    C.A. Shaffer and H. Samet. Set operations for unaligned linear quadtrees. Computer Vision, Graphics, and Image Processing, 50(1):29–49, April 1990.Google Scholar
  15. [SSN90]
    C.A. Shaffer, H. Samet, and R.C. Nelson. Quilt: A geographic information system based on quadtrees. International Journal of Geographic Information Systems, 4(2):103–131, August 1990.Google Scholar
  16. [SW89]
    H. Samet and R.E. Webber. A comparison of the space requirements of multi-dimensional quadtree-based file structures. Visual Computer, 5(6):349–359, December 1989.Google Scholar
  17. [SPMA87]
    T.R. Smith, D.J. Peuquet, S. Menon and P. Agarwal. KBGIS-II: A knowledge-based geographical information system. International Journal of Geographical Information Systems, 1(2):149–172, April 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Clifford A. Shaffer
    • 1
  • Patrick R. Brown
    • 2
  1. 1.Department of Computer ScienceVirginia TechBlacksburg
  2. 2.IBM CorporationKingston

Personalised recommendations