Abstract
Nested data cubes (NDCs in short) are a generalization of other OLAP models such as f-tables [4] and hypercubes [2], but also of classical structures as sets, bags, and relations. This model adds to the previous models flexibility in viewing the data, in that it allows for the assignment of priorities to the different dimensions of the multidimensional OLAP data.
We also present an algebra in which most typical OLAP analysis and navigation operations can be formulated. We present a number of algebraic operators that work on nested data cubes and that preserve the functional dependency between the dimensional coordinates of the data cube and the factual data in it. We show how these operations can be applied to sub-NDCs at any depth, and also show that the NDC algebra can express the SPJR algebra [1] of the relational model. Importantly, we show that the NDC algebra primitives can be implemented by linear time algorithms.
Post-doctoral research fellow of the Fund for Scientific Research of Flanders (FWO).
Affiliated to the University of Brussels (VUB) at the time this research was done.
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References
S. Abiteboul, R. Hull, V. Vianu. Foundations of Databases. Addison-Wesley, 1995.
R. Agrawal, A. Gupta, and S. Sarawagi. Modeling multidimensional databases. In Proc. IEEE Int. Conf. Data Engineering (ICDE ‘87), pages 232–243, 1997.
M. Blaschka, C. Sapia, G. Höfling, and B. Dinter. Finding Your Way through Multidimensional Data Models. In DWDOT Workshop (Dexa 98), Vienna, 1998.
L. Cabibbo and R. Torlone. Querying multidimensional databases. In Sixth Int. Workshop on Database Programming Languages (DBPL ‘87), pages 253–269, 1997.
S. Chaudhuri and U. Dayal. An overview of data warehousing and olap technology. SIGMOD Record, 26 (1): 65–74, 1997.
E. Codd, S. Codd, and C. Salley. Providing OLAP (On-Line Analytical Processing) to user-analysts: An IT mandate. Arbor Software White Paper.
G. Colhat. Olap, relational, and multidimensional database systems. SIGMOD Record, 25 (3): 64–69, 1996.
S. Dekeyser, B. Kuijpers, J. Paredaens, and J. Wijsen. Nested Data Cubes. Technical Report 9804, University of Antwerp, 1998. ftp://wins.uia.ac.be/pub/olapindc.ps
C. Dyreson. Information retrieval from an incomplete data cube. In Proc. Int. Conf. Very Large Data Bases (VLDB ‘86), pages 532–543, Bombai, India, 1996.
Essbase. Arbor Software, http://www.arborsoft.com/OLAP.html.
P.C. Fischer, and S.J. Thomas. Nested Relational Structures. In The Theory of Databases, Advances in Computing Research III, PC. Kanellakis, ed., pages 269–307, JAI Press, Greenwich, CT, 1986.
J. Gray, A. Boswirth, A. Layman, and H. Pirahesh. Data cube: A relational aggregation operator generalizing group-by. In Proc. IEEE Int. Conf. Data Engineering (ICDE ‘87), pages 152–159, 1997.
J. Gray, S. Chaudhuri, A. Boswirth, A. Layman, D. Reichart, F. Pellow, and H. Pirahesh. Data cube: A relational aggregation operator generalizing group-by, cross-tab, and sub-totals. Data Mining and Knowledge Discovery, 1: 29–53, 1997.
M. Gyssens, L. Lakshmanan, and I. Subramanian. Tables as a paradigm for querying and restructuring. In Proc. Symposium on Principles of Database Systems (PODS ‘86), pages 93–103, Montreal, Canada, 1996.
M. Gyssens and L. Lakshmanan. A Foundation for Multi-Dimensional Databases. In Proc. VLDB ‘87, pages 106–115, Athens, Greece, 1997.
J. Han. OLAP mining: An integration of OLAP with data mining. In Proceedings of the 7th IFIP 2.6 Working Conf. on Database Semantics (DS-7), pages 1–9, 1997.
V. Harinarayan, A. Rajaraman, and J. D. Ullman. Implementing data cubes efficiently. In Proc. ACM SIGMOD International Conference on Management of Data (SIGMOD ‘86), pages 205–216, Montreal, Canada, 1996.
G. Jaeschke, and H.-J. Schek. Remarks on the Algebra on Non First Normal Form Relations. In Proceedings first Symposium on Principles of Database Systems (PODS ‘82), pages 124–138, Los Angeles, CA, 1982.
Intelligent server. IBM, http://www.software.ibm.corn/data/pubs/papers.
W. Lehner. Modeling Large Scale OLAP Scenarios. In Proceedings of EDBT ‘88, pages 153–167, Valencia, Spain, 1998.
L. Libkin, R. Machlin, and L. Wong. A query language for multidimensional arrays: Design implementation, and optimization techniques. In Proc. Int. Conf. Management of Data (SIGMOD ‘86), pages 228–239, Montreal, Canada, 1996.
A. Marathe and K. Salem. A language for manipulating arrays. In Proc. Int. Conf. Very Large Data Bases (VLDB ‘87), pages 46–55, Athens, Greece, 1997.
Pilot decision support suite. Pilot Software, rickover.pilotsw.com/products/.
Red brick warehouse. Red Brick, www.redbrick.com/rbs-g/html/plo.html.
Sales analyzer. Oracle, http://www.oracle.com/products/olap/html/.
S. Sasawagi and M. Stonebraker. Efficient organization of large multidimensional arrays. In Proc. Int. Conf. Data Engineering, pages 328–336, Houston, TX, 1994.
H. J. Schek, and M. H. Scholl. The Relational Model with Relation-Valued Attributes. In Information Systems 11:2, pages 137–147, 1986.
A. Shoshani. OLAP and statistical databases: Similarities and differences. In Proc. ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS ‘87), pages 185–196, Tucson, AZ, 1997.
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Dekeyser, S., Kuijpers, B., Paredaens, J., Wijsen, J. (1999). Nested Data Cubes for OLAP. In: Kambayashi, Y., Lee, D.L., Lim, EP., Mohania, M.K., Masunaga, Y. (eds) Advances in Database Technologies. ER 1998. Lecture Notes in Computer Science, vol 1552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-49121-7_11
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DOI: https://doi.org/10.1007/978-3-540-49121-7_11
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