L. Cabibbo and R. Torlone. Querying multidimensional databases. In Proceedings of the 6th International Workshop on Database Programming Languages, East Park, Colorado, USA, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....al. 1997, Gyssens et al. 1997, Jagadish et al. 1999, Kimball, 1996, Li et al. 1996] are close to the relational SQL data model and query language, but do not support advanced features such as automatic aggregation, irregular hierarchies, and correct aggregation. Second, the simple cube models [Cabibbo et al. 1997, Lehner, 1998, Rafanelli et al. 1990, Thomsen, 1999, Vassiliadis, 1998] are pure multidimensional models, meaning that their data model is not relational like and they cannot be queried using SQL. Also, they do not handle the full spectrum of irregular hierarchies, automatic aggregation, and ....

L. Cabibbo and R. Torlone. Querying Multidimensional Databases. In Proceedings of the Sixth International Conference on Database Programming Languages, pp. 319--335, 1997.

....Condition (C2) states that each member in a category reaches no more than one member in any category above it. A dimension satisfying this restriction is also referred to as being partitioned [6] or being strict [13] Condition (C2) appears as an inherent constraint in most dimension models [3, 11]. Condition (C3) states that the member sets are pairwise disjoint. This condition avoids redundant aggregates in the datacube. Condition (C4) says that all is the only member in MembSet al..l . Condition (C5) states that a member cannot be a parent and an indirect ancestor of another member at the ....

L. Cabibbo and R. Torlone. Querying multidimensional databases. In Proceedings of the 6th International Workshop on Database Programming Languages, East Park, Colorado, USA, 1997.

....dimensions, which leads to the formalism of RUD with negation (RUD : A complete axiomatization for reasoning about RUD : is given. 1 Introduction Recently, there has been a lot of interest in OLAP and data mining. In these domains, generalization hierarchies play an important role [5, 8, 10, 14]. A typical example is the time hierarchy, where years are partitioned into months, months into days, and so on. Nevertheless, many other hierarchies have been exemplified in the literature; for example, the earth surface can be partitioned into continents, countries, states, and so on. Also ....

....in a year; we say that every month rolls up to its year. This is denoted MONTH YEAR, and there is a function mapping every month to the year it belongs to. On the other hand, in Figure 1, hexagons do not divide evenly into Voronoi cells, nor vice versa. The following definition is adapted from [5]. Definition 1 We assume the existence of a partially ordered set (L; of levels. Every level L of L has associated with it a set of values, denoted ext(L) A roll up instantiation U is a set of functions as follows: for every L 1 ; L 2 2 L with L 1 L 2 , there is a total function, denoted U ....

L. Cabibbo and R. Torlone. Querying multidimensional databases. In Sixth Int. Workshop on Database Programming Languages, pages 253--269, 1997.

....each of these categories, we present the typical way of modeling the information. 2.1. The multidimensional nature 2.1.1. User s needs The effectiveness of analysis based on OLAP is related to the ability to describe and manipulate data under a form close to the vision of the analyst [CHA 97, CAB 97] The simple relational modeling becomes inappropriate in the context of multidimensional data. The intuition underlying this multidimensional modeling is to consider a multidimensional data as a point in a multidimensional space. In this context, CAB 97] suggests defining dimension as a ....

....to the vision of the analyst [CHA 97, CAB 97] The simple relational modeling becomes inappropriate in the context of multidimensional data. The intuition underlying this multidimensional modeling is to consider a multidimensional data as a point in a multidimensional space. In this context, CAB 97] suggests defining dimension as a linguistic category used to characterize the structure of data according to a business perspective. Consider the relation depicted in Figure 1, that represents the 1996 part sales in four regions. Several linguistic categories can be found in these data, each ....

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CABIBBO L., TORLONE R., "Querying Multidimensional Databases", Proc. 6th DBPL, Estes Park, CO, Aug. 1997.

....Finally, section 5 presents some conclusions and a summary table with all the models presented in this paper. 2 Related work In [BSHD98] a list of requirements for a formal model in order to be suitable for OLAP applications, is used to analyze the seven models found in [AGS97] LW96] GL97] [CT97], Vas98] Leh98] and [DT97] which are chosen because they contain some kind of formalism. Those requirements (derived from general design principles, and from characteristics of OLAP applications) are the following: Explicit separation of cube structure and its contents Complex ....

....They are defined as a linear hierarchy of Dimension Levels (called classification attributes) at IL, and the instances of each Dimension Level have associated Classification Attributes (called classification nodes) at LL. Cabibbo and Torlone (MD) Cabibbo and Torlone, in [CT98a] CT98b] and [CT97], qualify their model MD as logical . However, they say that it is independent of any specific implementation, and present a design methodology to obtain an MD scheme from an E R one. Moreover, it is also said that MD is at a higher level of abstraction than a star scheme consisting of relational ....

L. Cabibbo and R. Torlone. Querying multidimensional databases. In Proc. of 6th Int. Workshop on Database Programming Languages (DBPL6), Estes Park (USA), 1997.

....patient. Symptom Table DiagnosisID SymptomID 80 91 81 91 82 90 82 92 Diagnosis Symptoms Table Table 3: Data for the Epidemiology Database multidimensional data model and query language are equivalent in expressive power to previous approaches such as the ones proposed by Cabbibo et al. [3] and Jagadish et al. 19] The ODB data model and query language is the ODMG data model and OQL query language. 3.1 Summary Data Model The model has constructs for defining the schema, the instances, and the aggregation properties. An n dimensional fact schema is a two tuple 99 , ....

L. Cabibbo and R. Torlone. Querying Multidimensional Databases. In Proceedings of the Sixth International Conference on Database Programming Languages, pp. 319--335, 1997.

....and multiple hierarchically organised dimensions can be abstracted and described could provide support for query languages in multidimensional data models. In fact, in the few attempts where a cube algebra introduces the notion of multiple dimensions and of levels within dimensions (e.g. [Cabibbo and Torlone, 1997]) the Data Warehouse Conceptual Schema could serve as a reference meta model for deriving the inter relations among levels and dimensions. Hacid and Sattler, 1997] presents a proposal for an extension of the cube algebra introduced in [Agrawal et al. 1995] which makes explicit use of ....

Luca Cabibbo and Riccardo Torlone. Querying multidimensional databases. In proc. Sixth Int. Workshop on Database Programming Languages (DBPL-97), pages 253--269, 1997.

....ODB components. The multidimensional model precisely and concisely captures core multidimensional concepts such as categories, dimensions, and automatic aggregation. The model and query language are equivalent in expressive power to previous approaches such as the ones proposed by Cabbibo et al. [2] and Jagadish et al. 12] The ODB data model and query language is the ODMG data model and OQL query language. 3.1 Summary Data Model The model has constructs for defining the schema, the instances, and the aggregation properties. An n dimensional fact schema is a two tuple S = F ; D) where ....

L. Cabibbo and R. Torlone. Querying Multidimensional Databases. In Proceedings of DBPL, pp. 319--335, 1997.

....scenarios. A key aspect of multidimensional data is the separation of factual and dimensional data. While dimensions represent descriptive and relatively static data, facts depict eventbased data, represented as points in spaces defined by dimensions. A number of multidimensional models for OLAP [CT97] HMV99a] LAW98] JLS99] have recently incorporated dimensions as first class entities in query and update languages. In the logical layer, a dimension is composed of a schema and an instance. The dimension schema includes a directed acyclic graph (DAG) of levels, called hierarchy schema, where ....

....instance consists of a set of members for each level, called member sets; and a hierarchy relation that models the ancestor descendant relation between the members. For instance, we may have T oronto as a member of a level City in a dimension representing locations. In most of the models [CT97] HMV99a] HMV99b] the hierarchy relation is represented by a set of functions between member sets, called rollup functions. Usually, we say that a level l 1 rolls up to another level l 2 when there exists an edge from l 1 to l 2 in the hierarchy, meaning that there is a rollup function from l 1 ....

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L. Cabibbo and R. Torlone. Querying multidimensional databases. In Proceedings of the 6th DBPL Workshop, East Park, Colorado, USA, 1997.

....hierarchically organised dimensions can be abstracted and described can be used in query languages and for semantic optimization in multidimensional data bases. In fact, in the few attempts where a cube algebra introduces the notion of multiple dimensions and of levels within dimensions (e.g. [Cabibbo and Torlone, 1997, Vassiliadis, 1998] the Data Warehouse Conceptual Schema can serve as a reference meta model for deriving the inter relations among levels and dimensions. Let us now consider a concrete example related to the analysis of the average duration of telephone calls according to their dates and ....

Cabibbo, Luca and Torlone, Riccardo 1997. Querying multidimensional databases. In proc. Sixth Int. Workshop on Database Programming Languages (DBPL-97). 253--269. E. Franconi, U. Sattler 13-9

....multiple hierarchically organised dimensions can be abstracted and described could provide support for query languages in multidimensional data models. In fact, in the few attempts where a cube algebra introduces the notion of multiple dimensions and of levels within dimensions #e.g. #Cabibbo and Torlone, 1997## the Data Warehouse Conceptual Schema could serve as a reference meta model for deriving the inter relations among levels and dimensions. #Hacid and Sattler, 1997# presents a proposal for an extension of the cube algebra introduced in #Agrawal et al. 1995#, which makes explicit use of ....

Torlone. Querying multidimensional databases. In proc. Sixth Int. Workshop on Database Programming Languages #DBPL-97#, pages 253#269, 1997.

....show how this surplus expressiveness can be introduced in non temporal dimensions, which leads to the formalism of RUD with negation (RUD : A complete axiomatization for reasoning about RUD : is given. 1 Introduction Generalization hierarchies play an important role in OLAP and data mining [5, 6, 8]. Along the spatial dimension, for example, countries are divided into states, states into cities, and so on. Each of these levels can be used to aggregate spacerelated data, such as census data. Recently, several database researchers have focused on one particular generalization hierarchy called ....

....a fiscal year, respectively. It is correct to conclude from this that the price cannot change within a week. That is, D WEEK Price . The extension of RUDs proposed in Sect. 3 allows us to express collectively finer than in our framework. 2. 2 Roll Up The following definition, adapted from [5], defines roll up. Definition 1. We assume the existence of a partially ordered set (L; of levels . Every level L of L has associated with it a set of values, denoted ext(L) A roll up instantiation U is a set of functions as follows: for every L 1 ; L 2 2 L with L 1 L 2 , there is a total ....

L. Cabibbo and R. Torlone. Querying multidimensional databases. In Sixth Int. Workshop on Database Programming Languages, pages 253--269, 1997.

....hierarchically organised dimensions can be abstracted and described can be used in query languages and for semantic optimization in multidimensional data bases. In fact, in the few attempts where a cube algebra introduces the notion of multiple dimensions and of levels within dimensions (e.g. [Cabibbo and Torlone, 1997; Vassiliadis, 1998] the Data Warehouse Conceptual Schema can serve as a reference meta model for deriving the inter relations among levels and dimensions. Let us now consider a concrete example related to the analysis of the average duration of telephone calls according to their dates and ....

Cabibbo, Luca and Torlone, Riccardo 1997. Querying multidimensional databases. In proc. Sixth Int. Workshop on Database Programming Languages (DBPL-97). 253--269.

....development of the systems as opposed to the relational systems which are all based on the same relational data model. The lack of a formal multidimensional data model has attracted the interest of several researches for the past years. This results in a multitude of different formal models. [10], 17] 2] 38] 27] are the most well known approaches. In this context extensions of the classical multidimensional model have been proposed. 26] gives a formal model incorporating feature attributes for dimension members. 11] introduce the notion of nested multidimensional data cubes. An ....

L. Cabbibo,and R. Torlone, "Querying Multidimensional Databases", Proc. DBPL, 1997

....Despite its importance, conceptual design is one of the less discussed subjects within the DW literature. In fact, besides our early works [9] 10] only few papers focus on this issue. In [6] the authors propose as a conceptual model an extension of the multidimensional model described in [4]; a declaratory query language is introduced and its expressiveness is evaluated. However, fact tables are used to support conceptual design, thus blurring the borders between conceptual and logical design. In [22] an object oriented model called Nested Multidimensional Data Model has been ....

L. Cabibbo, and R. Torlone, "Querying Multidimensional databases", 6 th Workshop on Database Programming Languages (DBPL'97), 1997.

....forms the basis for an optimization for computing the so called hierarchical CUBE that they introduce. Neither of the above two works addresses the technical issues in modeling or querying dimension hierarchies, two novel aspects of our contributions. On the theoretical side, Cabibbo and Torlone [3] propose a model for multi dimensional databases. Hurtado et al. 10] build on that model, and address the issue of maintaining materialized views on a data warehouse against updates to dimensions; this issue is completely orthogonal to the objective of this paper. Their models give a first class ....

....correspond a tuple in the parent (ancestor) table such that the hierarchical values in these two tuples are related by the child parent (descendant ancestor) relationship. It can be seen that our notion of hierarchy closely corresponds to the notion of hierarchy schema and instance as defined in [3, 10]. The main difference is that we do not assume that nodes (levels) in a hierarchy schema are necessarily named (although our examples show such names, for convenience) We are now ready to formalize the notion of a dimension. Definition 3.4 [Dimension] A dimension schema D(H) is a name D ....

L. Cabibbo and R. Torlone. Querying multidimensional databases. In Proceedings of the 6th DBPL Workshop, pages 253--269, 1997.

....and dollar. The family of all levels is a partially ordered set. The order is denoted , and corresponds to an is finer than relationship. For example, we have day week, and there is a many to one mapping that maps each day to the week it belongs to. The following definition is adapted from [2]. Definition 1 We assume the existence of a finite, partially ordered set (L; of levels. Every level l 2 L has associated with it a domain of constants, denoted dom(l) such that distinct levels have disjoint domains. A roll up instantiation is a set I of functions as follows: For every l 1 ; ....

L. Cabibbo and R. Torlone. Querying multidimensional databases. In Sixth Int. Workshop on Database Programming Languages, pages 253--269, 1997.

.... Jan Paredaens, and Jef Wijsen University of Antwerp (UIA) Dept. Math. Computer Sci. Universiteitsplein 1, B 2610 Antwerp, Belgium Email: fdekeyser,kuijpers,pareda,jwijseng uia.ua.ac.be Abstract. Nested data cubes (NDCs in short) are a generalization of other OLAP models such as f tables [3] 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 ....

....for OLAP systems: the tabular database model. They give a complete algebraic language for querying and restructuring two dimensional tables. Agrawal et al. 2] have introduced a hypercube based data model with a number of operations that can be easily inserted into SQL. Cabibbo and Torlone [3] have recently proposed a data model that forms a logical counterpart of multidimensional arrays. Their model is based on dimensions and f tables. Dimensions are partially ordered categories that correspond to different ways of looking at the multidimensional information (see also [8] F tables ....

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L. Cabibbo and R. Torlone. Querying multidimensional databases. In Sixth Int. Workshop on Database Programming Languages (DBPL '97), pages 253--269, 1997.

....OLAP Stijn Dekeyser Bart Kuijpers Jan Paredaens Universiteit Antwerpen (UIA) y Jef Wijsen Vrije Universiteit Brussel (VUB) z Abstract 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 ....

....for OLAP systems: the tabular database model. They give a complete algebraic language for querying and restructuring two dimensional tables. Agrawal et al. 2] have introduced a hypercube based data model with a number of operations that can be easily inserted into SQL. Cabibbo and Torlone [3] have recently proposed a data model that forms a logical counterpart of multidimensional arrays. Their model is based on dimensions and f tables. Dimensions are partially ordered categories that correspond to different ways of looking at the multidimensional information (see also [7] F tables ....

[Article contains additional citation context not shown here]

L. Cabibbo and R. Torlone. Querying multidimensional databases. In Sixth Int. Workshop on Database Programming Languages, pages 253--269, 1997.

....under them, are poorly supported (or not supported at all) in current commercial systems. Our focus in this paper has been to introduce the problem and present a framework for it. Several multidimensional models have already been presented [9, 12, 2] We chose the work by Cabibbo and Torlone [3] as a starting point for our model. We developed a set of operators for structural and instance updates over dimensions. We also presented algorithms to perform maintenance when using ROLAP storage of the data cube, under both structural and instance updates. Mumick et al. [14] proposed the ....

L. Cabibbo and R. Torlone. Querying multidimensional databases. In Proceedings of the 6th International Workshop on Database Programming Languages, pages 253--269, East Park, Colorado, USA, 1997.

....row, for example, indicates that at Allen s, the price of yellow hinges amounted to 10 dollars in January. The data cube may be called incomplete, as certain values are missing; for example, at Allen s there were no red hinges in January. This tabular representation has also been called an f table [1]. Such tables are flat, and consequently, can cause some perceptional difficulties: ffl The dimensionality can be too high to be practically visualizable in a cubic format. The example table of figure 1 (top) has dimensionality=4. ffl The cardinality can be large. The example table of figure ....

L. Cabibbo and R. Torlone. Querying multidimensional databases. In Sixth Int. Workshop on Database Programming Languages, pages 253--269, 1997.

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L. Cabibbo and R. Torlone. Querying multidimensional databases. In Sixth Int. Workshop on Database Programming Languages (DBPL'97), Springer-Verlag, 1997.

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L. Cabibbo and R. Torlone. Querying multidimensional databases. In 6th Int. Workshop on Database Programming Languages #DBPL'97#, 1997.

....description of business data, independent of the way in which data is stored. In this paper we study conceptual and practical issues related to the design of multidimensional databases. The framework for our investigation is MD, a logical model for OLAP systems that extends an earlier proposal [3]. This model includes a number of concepts that generalize the notions of dimensional hierarchies, fact tables, and measures, commonly used in commercial systems. In MD, dimensions are linguistic categories that describe different ways of looking at the information. Each dimension is organized ....

....making. Further discussion on OLAP, multidimensional analysis, and data warehousing can be found in [4, 8, 9, 12] Recently, Mendelzon has published a comprehensive on line bibliography on this subject [10] The MD model illustrated in this paper extends the multidimensional model proposed in [3]. While the previous paper is mainly oriented to the introduction of a declarative query language and the investigation of its expressiveness, the present paper is focused on the design of multidimensional databases. The traditional model used in the context of OLAP systems is based on the notion ....

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L. Cabibbo and R. Torlone. Querying multidimensional databases. In 6th Int. Workshop on Database Programming Languages (DBPL'97), 1997.

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L. Cabibbo and R. Torlone. Querying multidimensional databases. In Proceedings of the 6th International Workshop on Database Programming Languages, East Park, Colorado, USA, 1997.

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L. Cabibbo and R. Torlone. Querying multidimensional databases. In Proceedings of the 6th International Workshop on Database Programming Languages, East Park, Colorado, USA, 1997.

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L. Cabibbo and R. Torlone. Querying multidimensional databases. In Proceedings of the 6th International Workshop on Database Programming Languages, East Park, Colorado, USA, 1997.

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Cabibbo L., Torlone R., Querying Multidimensional Databases, Proc. of the 6th DBPL Workshop, 1997.

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