Abstract
A fundamental problem In the area of database systems Is the retrieval of data satisfying certain criteria. The simplest such problem Is the retrieval of data based on a single key, and a comprehensive treatment of this problem Is contained In Knuth[1]. A more difficult problem Is the retrieval of data based on criteria for several keys, the so-called multidimensional search problem. Suppose that each of n records of a file contains a fixed number, d , of keys. A query asks for all records for which the d keys satisfy certain criteria. For example, upper and lower bounds maybe specified for some or all keys, yielding the socalled orthogonal range query problem.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
D. E. Knuth, The Art of Computer Programming, Vol 8: Sorting and Searching ,Addlson-Wesley, Reading, MA, 1973.
J.L. Bentley and J. H. Friedman, “Data Structures for Range Searching,” Comp. Surveys ,vol. 11, pp. 397–409, 4, 1979.
M. Irl et al., “Fundamental Algorithms for Geographic Data Processing,” Operations Research Society of Japan ,vol. TR 83-1, (In Japanese), 1983.
D. E. Wlllard, “Polygon Retrieval,” SIAM Journal on Computing ,vol. 11, pp. 149–165, 1982.
F. Yao, “3-Space Partition and Its Applications,” In Proceedings of the 15th STOC ,pp. 258–263, A.C.M., Boston, Massachusets , 1983.
R.A. Flnkel and J. L. Bentley, “Quad Trees: A Data structure for retrelval on composite keys,” Acta Informatica ,vol. 4, pp. 1–9, 1974.
M. H. Overmars and J. van Leeuwen, “Dynamic Multl-Dlmenslnal Data Structures Based on Quad-and K-D Trees,” Acta Informatica ,vol. 17, pp. 267–285, 1982.
J. L. Bentley, “Multidimensional Binary Search Trees used for Associative Searching,” Comm. ACM ,vol. 18, pp. 509–517, 1975.
J. B. Rothnle and T. Lozano, “Attribute Based File Organization In Paged Memory Environment,” Comm. of ACM ,vol. 17, pp. 63–69, 2, 1974.
J. H. Llou and S. B. Yao, “Multidimensional Clustering for Data Base Organization,” Information Systems ,vol. 2, pp. 187–198, 1977.
T. Merrett, “Multidimensional Paging for Efficient Data Base Querying,” In Proc. Int. Conf. on Management of Data, ICMOD ,pp. 277–290, mllano, 1978.
E. J. Otoo, “Low Level Structures In the Implementation of the Relational Algebra,” SOCS 83.17, McGill University, School of Computer Science, August 1983.
H. Edelsbrunner and E. Welzl, “Halfplane Range Search In Linear Space and O (n 0.695) Query Time,” Fill, Technical University of Graz , 1982.
I.M. Yaglom and V.G. Boltyanskll, Convex Figures ,Holt, Rlnehart and Winston, 1961.
B. Mendelson, Introduction to Topology ,Allyn & Bacon, Boston, 1962.
F. Yao, Private Communication ,1983.
D.P. Dobkln and H. Edelsbrunner, “Space Searching for Intersecting Objects,” In Proceedings of the 25th FOCS ,pp. 387–391, IEEE, Ocober, 1984.
D. Avis, “Non-Partltlonable Point Sets,” Information Proc. Letters ,vol. 19, pp. 125–129, 1984.
D. Gale, “Neighborly and Cyclic Polytopes,” Proceedings of the Symp. in Pure Mathematics ,vol. 7, pp. 225–232, 1963.
E. N. Gilbert, “Gray Codes and Paths on the n-cube,” Bell System Technical Journal ,pp. 815–826, 1958.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Plenum Press, New York
About this chapter
Cite this chapter
Avis, D. (1987). Space Partitioning and Its Application to Generalized Retrieval Problems. In: Ghosh, S.P., Kambayashi, Y., Tanaka, K. (eds) Foundations of Data Organization. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1881-1_20
Download citation
DOI: https://doi.org/10.1007/978-1-4613-1881-1_20
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4612-9048-3
Online ISBN: 978-1-4613-1881-1
eBook Packages: Springer Book Archive