Abstract
Recently multidimensional arrays have received considerable attention among the database community, applications ranging from GIS to OLAP. Work on the formalization of arrays frequently focuses on mapping sparse arrays to ROLAP schemata. Database modeling of further array types, such as image data, is done differently and with less rigid methods. A unifying formal framework for general array handling of image, sensor, statistics, and OLAP data is missing.
We present a cross-dimensional and application-independent algebra for the high-level treatment of arbitrary arrays. An array constructor, a generalized aggregate, plus a multidimensional sorter allow to declaratively manipulate arrays. This algebra forms the conceptual basis of a domain-independent array DBMS, RasDaMan, which offers an SQL-based query language with extensive algebraic query and storage optimization. The system is in practical use in neuro science.
We introduce the algebra and show how the operators transform to the array query language. The universality of our approach is demonstrated by a number of examples from imaging, statistics, and OLAP.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. Kimball: The Data Warehouse Toolkit. John Wiley & Sons, 1996
R. Haskin, R. Lorie: On Extending the Functions of a Relational Database System. Proc. ACM SIGMOD, Orlando, USA, June 1982, pp. 207–212.
R. Agrawal, A. Gupta, S. Sarawagi: Modeling Multidimensional Databases. Proc. 13th ICDE, Birmingham, UK, April 1997, pp. 232–243.
J Gray, A. Bosworth, A. Layman, H. Pirahesh: Data Cube: A Relational Aggregation Operator Generalizing Group-By, Cross-Tabs, and Sub-Totals. Technical Report MSRTR-95-22, Microsoft Research, Advance Technology Division, Microsoft Corp., November 1995.
A. Bauer, W. Lehner: The Cube-Query-Language for Multidimensional Statistical and Scientific Database Systems. Proc. 5th DASFAA 1997, Melbourne, Australia, April 1997, pp. 263–272.
A. Shoshani: Statistical Databases: Characteristics, Problems, and some Solutions. Proc. VLDB 8, Mexico City, Mexico, September 1982, pp. 208–222.
A. Shoshani: OLAP and Statistical Databases: Similarities and Differences. Proc. PODS 16, Tucson, USA,May 1997, pp. 185–196.
E.F. Codd, S.B. Codd, C.T. Salley: Providing Olap (On-Line Analytical Processing) to User-Analysts: An IT Mandate. White paper, 1995, URL: http://www.arborsoft.com/papers/coddTOC.html
L. Cabibbo, R. Torlone: A Logical Approach to Multidimensional Databases. EDBT 1998.
C. Li and X.S. Wang: A data model for supporting on-line analytical processing. Proc. CIKM, Rockville, USA, November 1996, pp. 81–88.
Marc Gyssens, Laks,V.S. Lakshmanan: A Foundation for Multi-Dimensional Databases. Proc. VLDB, Athens, Greece, August 1997, pp. 106–115.
L. Libkin, R. Machlin, L. Wong: A Query Language for Multidimensional Arrays: Design, Implementation, and Optimization Techniques. Proc. ACM SIGMOD, Montreal, Canada, June 1996, pp. 228–239.
A.P. Marathe, K. Salem: A Language for Manipulating Arrays. Proc. VLDB, Athens, Greece, August 1997, pp. 46–55.
P. Buneman: The Discrete Fourier Transform as a Database Query. Technical Report MSCIS-93-37, University of Pennsylvania, 1993.
P. Baumann: On the Management of Multidimensional Discrete Data. VLDB Journal 4(3)1994, Special Issue on Spatial Database Systems, pp. 401–444.
P. Baumann: Language Support for Raster Image Manipulation in Databases. Proc. Int. Workshop on Graphics Modeling and Visualization in Science & Technology, Darmstadt, Germany, April 1992.
N. Widmann, P. Baumann: Performance Evaluation of Multidimensional Array Storage Techniques in Databases. Proc. IDEAS, Montreal, Canada, June 1999 (accepted for publication)
G. Ritter, J. Wilson, J. Davidson: Image Algebra: An Overview. Computer Vision, Graphics, and Image Processing, 49(1)1994, pp. 297–336.
M. Stonebraker, D. Moore: Object-Relational DBMSs: The Next Great Wave. Morgan Kaufmann Publishers, 1996.
R.G.G. Cattell: The Object Database Standard: ODMG-93. Morgan Kaufmann Publishers, 1996.
R. Ritsch, P. Baumann: Optimization and Evaluation of Array Queries. RasDaMan Project Technical Report, FORWISS 1998.
M. Blaschka, C. Sapia, G. Höfling, B. Dinter: Finding Your Way through Multidimensional Data Models. Proc. Workshop on Data Warehouse Design and OLAP Technology DWDOT, Vienna, Austria, August 1998.
K.E. Iverson: A Programming Language. John Wiley & Sons, Inc., New York, 1962
J.A. Brown, H.P. Crowder: APL2: Getting Started. IBM Systems Journal, Vol. 30No. 4, 1991, pp. 433–445
S. Vandenberg, D. De Witt: Algebraic Support for Complex Objects with Arrays, Identity, and Inheritance. Proc. ACM SIGMOD, Denver, USA, May 1991, pp. 158–167.
A. Datta, H. Thomas: A Conceptual Model and an Algebra for Online-Analytical Processing in Data Warehouses. Proc. WITS 1997
W. Lehner: Modeling Large Scale OLAP Scenarios. Proc. 6th EDBT, Valencia, Spain, March 1998, pp. 153–167
P. Vassiliadis: Modeling Multidimensional Databases, Cubes, and Cube Operations. Proc. 10th SSDBM, Capri, Italy, July 1998
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Baumann, P. (1999). A Database Array Algebra for Spatio-Temporal Data and Beyond. In: Pinter, R.Y., Tsur, S. (eds) Next Generation Information Technologies and Systems. NGITS 1999. Lecture Notes in Computer Science, vol 1649. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48521-X_7
Download citation
DOI: https://doi.org/10.1007/3-540-48521-X_7
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66225-9
Online ISBN: 978-3-540-48521-6
eBook Packages: Springer Book Archive