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A Foundation for MultiDimensional Databases
, 1997
"... gyssensQcharlie.luc.ac.be laksQcs.concordia.ca We present a multidimensional database model, which we believe can serve as a conceptual model for OnLine Analytical Processing (OLAP)based applications. Apart from providing the functionalities necessary for OLAPbased applications, the main feat ..."
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Cited by 118 (0 self)
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gyssensQcharlie.luc.ac.be laksQcs.concordia.ca We present a multidimensional database model, which we believe can serve as a conceptual model for OnLine Analytical Processing (OLAP)based applications. Apart from providing the functionalities necessary for OLAPbased applications, the main feature of the model we propose is a clear separation between structural aspects and the contents. This separation of concerns allows us to define data manipulation languages in a reasonably simple, transparent way. In particular, we show that the data cube operator can be expressed easily. Concretely, we define an algebra and a calculus and show them to be equivalent. We conclude by comparing our approach to related work. The conceptual multidimensional database model developed here is orthogonal to its implementation, which is not a subject of the present paper. 1
A Data Model for Supporting OnLine Analytical Processing
, 1996
"... A database application, called "online analytical processing" (or OLAP) and aimed at providing business intelligence through online multidimensional data analysis, has become increasingly important due to the existence of huge amounts of online data. This paper formalizes a multidimensi ..."
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Cited by 65 (1 self)
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A database application, called "online analytical processing" (or OLAP) and aimed at providing business intelligence through online multidimensional data analysis, has become increasingly important due to the existence of huge amounts of online data. This paper formalizes a multidimensional data (MDD) model for OLAP, and develops an algebraic query language called grouping algebra. The basic component of the MDD model is a multidimensional cube, consisting of a number of relations (called dimensions) and for each combination of tuples (called a coordinate), one from each dimension, there is an associated data value. Each dimension is viewed as a basic grouping, i.e., each tuple in the dimension corresponds to the group consisting of all the coordinates that contain this tuple. In order to express user queries, relational algebra expressions are then extended to those on basic groupings for obtaining complex groupings, including orderoriented groupings (for expressing, e.g., cumula...
Abstract A Data Model for Supporting OnLine Analytical Processing*
"... A database application, called “online analytical processing ” (or OLAP) and aimed at providing businessintelligence through online multidimensional data analysis, has become increasingly important due to the existence of huge amounts of online data. This paper formalizes a multidimensional data ..."
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A database application, called “online analytical processing ” (or OLAP) and aimed at providing businessintelligence through online multidimensional data analysis, has become increasingly important due to the existence of huge amounts of online data. This paper formalizes a multidimensional data (MDD) model for OLAP, and develops an algebraic query language called grouping algebra. The basic component of the MDD model is a multidimensional cube, consisting of a number of relations (called dimensions) and for each combination of tuples (called a coordinate), one from each dimension, there is an associated data value. Each dimension is viewed as a basic grouping, i.e., each tuple in the dimension comesponds to the group consisting of all the coordinates that contain this tuple. In order to express user queries, relational algebra expressions are then extended to those on basic groupings for obtaining complex groupings, including orderoriented groupings (for expressing, e.g., cumulative sum). The paper then considers the environment where the multidimensional cubes are materialized views derived from base data situated at remote sites. A multidimensional cube algebra is introduced in order to facilitate the data derivation. The putpose of the paper is to establish a formal foundation for further research regarding databasesupport for OLAP applications. 1
Optimizing Statistical Queries by Exploiting Orthogonality and Interval Properties of Grouping Relations
"... A statistical query first manipulates source category data to build a target category in the form of a grouping relation and then performs statistical functions on the associated measurement data. In this paper, the attributes in a grouping relation are partitioned into pairwise disjoint sets, eac ..."
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A statistical query first manipulates source category data to build a target category in the form of a grouping relation and then performs statistical functions on the associated measurement data. In this paper, the attributes in a grouping relation are partitioned into pairwise disjoint sets, each called a dimension. A grouping relation is said to be orthogonal if it is equal to the cross product of the projections of itself on all the dimensions. Orthogonality is useful in searching for and using precomputed summaries on other categories. However, a grouping relation is sometimes not orthogonal, but rather kpartially orthogonal (i.e., the union of k orthogonal ones). It is shown that it is NPcomplete to decide if a grouping relation is kpartially orthogonal. The paper then gives an algorithm to derive partial orthogonality. Also investigated in this paper are interval properties of grouping relations useful for optimizing statistical queries. An algorithm is described to derive...