Abstract
We study the problem of pre-computing auxillary information to support on-line range queries for the sum and max functions on a datacube. For a d-dimensional datacube with size n in each dimension, we propose a data structure for range max queries with O((4L)d) query time and O((12L2 n 1/Lγ(n))d) update time where L∈ 1;... log n is a user- controlled parameter and γ(n) is a slow-growing function. (For example, γ(n)≤log* n and γ(24110) = 3.) The data structure uses O((6nγ(n)) d) storage and can be initialized in time linear to its size. There are three major techniques employed in designing the data structure, namely, a technique for trading query and update times, a technique for trading query time and storage and a technique for extending 1-dimensional data structures to d-dimensional ones. Our techniques are also applicable to range queries over any semi-group and group operation, such as min, sum and count.
This research was fully supported by a grant from the Research Grants Council of the Hong Kong SAR, China [Project No. 9040314 (RGC Ref. No. CityU 1159/97E)].
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
R. Agrawal, A. Gupta, and S. Sarawagi. Modeling multidimensional databases. In 13th International Conference on Data Engineering. IEEE, 1997.
J. L. Bentley and M. I. Shamos. A problem in multivariate statistics: algorithms, data structure and applications. In 15th Allerton Conference on Communications, Control and Computing, pages 193–201, 1977.
J.L. Bentley. Multidimensional binary search trees used for associative searching. Communications of the ACM, 18(9):509–517, 1975.
J.L. Bentley. Multidimensional divide-and-conquer. Communications of the ACM, 23(4):214–228, April 1980.
J.L. Bentley and H.A. Maurer. Efficient worst-case data structures for range searching. Acta Informatica, 13:155–168, 1980.
A. Bolour. Optimal retrival algorithms for small region queries. SIAM Journal on Computing, 10(4):721–741, November 1981.
C.Y. Chan and Yannis E. Ioannidis. Hierarchical prefix cubes for range-sum queries. In Proceedings of ACM International Conference on Very Large Data Bases, pages 675–686, 1999.
Bernard Chazelle. Filtering search: A new approach to query-answering. SIAM Journal on Computing, 15(3):703–724, August 1986.
Bernard Chazelle. A functional approach to data structures and its use in multidimensional searching. SIAM Journal on Computing, 17(3):427–462, June 1988.
Bernard Chazelle. Lower bounds for orthogonal range searching: I. the reporting case. Journal of the ACM, 37(2):200–212, April 1990.
Bernard Chazelle. Lower bounds for orthogonal range searching: II. the arithmetic model. Journal of the ACM, 37(3):439–463, July 1990.
Bernard Chazelle and Burton Rosenberg. Computing partial sums in multidimensional arrays. In 5th Annual Symposium on Computational Geometry, pages 131–139, 1989.
D.W. Cheung, B. Zhou, B. Kao, K. Hu, and S.D. Lee. DROLAP-a dense-region based approach to on-line analytical processing. In 10th International Conference on Database and Expert Systems Applications (DEXA’99), 1999.
E.F. Codd. Providing OLAP (on-line analytical processing) to user-analysts: an IT mandate. Technical report, E.F. Codd and Associates, 1993.
The OLAP Council. MD-API the OLAP application program interface version 0.5 specification. Technical report, September 1996.
R.A. Finkel and J.L. Bentley. Quad trees: A data structure for retrievel on composite keys. Acta Informatica, 4:1–9, 1974.
Michael Fredman. A lower bound on the complexity of orthogonal range queries. Journal of the ACM, 28(4):696–705, 1981.
S. Geffner, D. Agrawal, A. El Abbadi, and T. Smith. Relative prefix sums: An efficient approach for querying dynamic olap data cubes. In 15th International Conference on Data Engineering, pages 328–335. IEEE, 1999.
Jim Gray, Adam Bosworth, Andrew Layman, and Hamid Pirahesh. Data cube: A relational aggregation operator generalizing group-by, cross-tab, and sub-totals. In 12th International Conference on Data Engineering, pages 152–159. IEEE, 1996.
Dov Harel and Robert Endre Tarjan. Fast algorithms for finding nearest common ancestors. SIAM Journal on Computing, 13(2):338–355, May 1984.
Ching-Tien Ho, Rakesh Agrawal, Nimrod Meggido, and Jyh-Jong Tsay. Techniques for speeding up rang-max queries. Technical report, IEEE Research Report, April 1997.
Ching-Tien Ho, Rakesh Agrawal, Nimrod Megiddo, and Ramakrishnan Srikant. Range queries in olap data cubes. In ACM SIGMOD Conference on the Management of Data, pages 73–88, 1997.
Ching-Tien Ho, Jehoshua Bruck, and Rakesh Agrawal. Partial-sum queries in olap data cubes using covering codes. IEEE Transactions on Computers, 47(12):1326–1340, 1998.
D.T. Lee and C.K. Wong. Worst-case analysis for region and partial region searches in multidimensional binary search trees and balanced quad trees. Acta Informatica, 9:23–29, 1977.
K.V. Ravi Kanth and Ambuj K. Singh. Efficient dynamic range searching using data replication. Technical Report TRCS97-12, University of California at Santa barbara, 1997.
Jean Vuillemin. A unifying look at data structures. Communications of the ACM, 23(4):229–239, 1980.
D.E. Willard. New data structures for orthogonal queries. SIAM Journal on Computing, 14(1):232–253, February 1985.
D.E. Willard and G.S. Lueker. Adding range restriction capability to dynamic data structures. Journal of the ACM, 32(3):597–617, July 1985.
Andrew Yao. On the complexity of maintaining partial sums. SIAM Journal on Computing, 14(2):277–288, May 1985.
Bo Zhou, David W. Cheung, and Ben Kao. A fast algorithm for density-based clustering in large database. In Methodologies for Knowledge Discovery and Data Mining (PAKDD’99), pages 338–349, 1999.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Keung Poon, C. (2001). Orthogonal Range Queries in OLAP. In: Van den Bussche, J., Vianu, V. (eds) Database Theory — ICDT 2001. ICDT 2001. Lecture Notes in Computer Science, vol 1973. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44503-X_23
Download citation
DOI: https://doi.org/10.1007/3-540-44503-X_23
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41456-8
Online ISBN: 978-3-540-44503-6
eBook Packages: Springer Book Archive