Characterization of hierarchies and some operators in OLAP environment (original) (raw)
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Hierarchies and relative operators in the OLAP environment
Sigmod Record, 2000
In the last few years, numerous proposals for modelling and querying Multidimensional Databases (MDDB) are proposed. A rigorous classification of the different types of hierarchies is still an open problem. In this paper we propose and discuss some different types of hierarchies within a single dimension of a cube. These hierarchies divide in different levels of aggregation a single dimension. Depending on them, we discuss the characterization of some OLAP operators that refer to hierarchies in order to maintain the data cube consistency. Moreover, we propose a set of operators for changing the hierarchy structure. The issues discussed provide modelling flexibility during the scheme design phase and correct data analysis.
Lecture Notes in Computer Science, 1999
We present a new model for OLAP, called the nested data cube (NDC) model. Nested data cubes are a generalization of other OLAP models such as f-tables [3], and hypercubes [2], but also of classical structures such as sets, bags, and relations. The model we propose adds to the previous models mainly 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 all 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. These operations include nesting, unnesting, summary, roll-up, and aggregation operations. We show how these operations can be applied to sub-NDC's at any depth, and also show that the NDC algebra can express the SPJR algebra [1] of the relational model. A major motivation for defining an algebra rather than a calculus, is that an algebra naturally leads to an implementation strategy. Importantly, we show that the NDC algebra primitives can be implemented by linear time algorithms.
Modeling multidimensional databases, cubes and cube operations
1998
On-Line Analytical Processing (OLAP) is a trend in database technology, which was recently introduced and has attracted the interest of a lot of research work. OLAP is based on the multidimensional view of data, supported either by multidimensional databases (MOLAP) or relational engines (ROLAP).
Hetero-homogeneous hierarchies in data warehouses
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Modelling and Optimisation Issues for Multidimensional Databases
Lecture Notes in Computer Science, 2000
It is commonly agreed that multidimensional data cubes form the basic logical data model for OLAP applications. Still, there seems to be no agreement on a common model for cubes. In this paper we propose a logical model for cubes based on the key observation that a cube is not a self-existing entity, but rather a view over an underlying data set. We accompany our model with syntactic characterisations for the problem of cube usability. To this end, we have developed algorithms to check whether (a) the marginal conditions of two cubes are appropriate for a rewriting, in the presence of aggregation hierarchies and (b) an implication exists between two selection conditions that involve different levels of aggregation of the same dimension hierarchy. Finally, we present a rewriting algorithm for the cube usability problem.
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Sigmod Record, 1999
In this paper, we present different proposals for multidimensional data cubes, which are the basic logical model for OLAP applications. We have grouped the work in the field in two categories: commercial tools (presented along with terminology and standards) and academic efforts. We further divide the academic efforts in two subcategories: the relational model extensions and the cube-oriented approaches. Finally,
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Proceedings of the 5th ACM international workshop on Data Warehousing and OLAP - DOLAP '02, 2002
When changes occur on data organization, conventional multidimensional structures are not adapted because dimensions are supposed to be static. In many cases, especially when time covered by the data warehouse is large, dimensions of the hypercube must be redesigned in order to integrate evolutions. We propose an approach allowing to track history but also to compare data, mapped into static structures. We define a conceptual model building a Mutiversion Fact the Temporal Multidimensional Schema and we introduce the notion of temporal modes of representation corresponding to different ways to analyze data and their evolution.
Efficient intensional redefinition of aggregation hierarchies in multidimensional databases
Proceedings of the 4th ACM international workshop on Data warehousing and OLAP - DOLAP '01, 2001
Enhancing multidimensional database models with aggregation hierarchies allows viewing data at different levels of aggregation. Usually, hierarchy instances are represented by means of so-called rollup functions. Rollup between adjacent levels in the hierarchy are given extensionally, while rollups between connected nonadjacent levels are obtained by means of function composition. In many real-life cases, this model cannot capture accurately the meaning of common situations, particularly when exceptions arise. Exceptions may appear due to corporate policies, unreliable data or uncertainty, and their presence may turn the notion of rollup composition unsuitable for representing real relationships in the aggregation hierarchies. In this paper we present a language allowing augmenting traditional extensional rollup functions with intensional knowledge. We denote this language IRAH (Intensional Redefinition for Aggregation Hierarchies). Programs in IRAH consist of intensional rules, which can be regarded as patterns for: (a) overriding natural composition between rollup functions on adjacent levels in the concept hierarchy, (b) canceling the effect of rollup functions for specific values. Our proposal is presented as a stratified default theory. We show that a unique model for the underlying theory always exists, and can be computed in a bottom-up fashion. Finally, we present an algorithm that computes the revised dimension in polynomial time, although under more realistic assumptions, complexity becomes linear on the number of paths in the hierarchy of the dimension instance.
Differentiated Multiple Aggregations in Multidimensional Databases
Lecture Notes in Computer Science, 2015
Many models have been proposed for modeling multidimensional data warehouses and most consider a same function to determine how measure values are aggregated according to different data detail levels. We provide a conceptual model that supports (1) multiple aggregations, associating to the same measure a different aggregation function according to analysis axes or hierarchies, and (2) differentiated aggregation, allowing specific aggregations at each detail level. Our model is based on a graphical formalism that allows controlling the validity of aggregation functions (distributive, algebraic or holistic). We also show how conceptual modeling can be used, in an R-OLAP environment, for building lattices of pre-computed aggregates.