Marc Gyssens

The powerset algebra as a result of adding programming constructs to the nested relational algebra

In this paper, we discuss augmentations of the nested relational algebra with programming constructs, such as while-loops and for-loops. We show that the algebras obtained in this way are equivalent to a slight extension of the powerset algebra, thus emphasizing both the strength and the naturalness of the powerset algebra as a tool to manipulate nested relations, and, at the same time, indicating more direct ways to implement this algebra.

A Decomposition Methodology for Cyclic Databases

A methodology is given to decompose a join dependency defined on a given relation scheme. The methodology works for acyclic as well as for cyclic join dependencies.

On the complexity of join dependencies

In [10] a method is proposed for decomposing join dependencies (jds) in a relational database using the notion of a hinge. This method was subsequently studied in [11] and [12]. We show how the technique of decomposition can be used to make integrity checking more efficient. It turns out that it is important to find a decomposition that minimizes the number of edges of its largest element. We show that the decompositions obtained with the method described in [10] are optimal in this respect. This minimality criterion leads to the definition of the degree of cyclicity, which allows us to classify jds and leads to the notion of n-cyclicity, of which acyclicity is a special case for n = 2. We then show that, for a fixed value of n (which may be greater than 2). integrity checking can be performed in polynomial time provided we restrict ourselves to n-cyclic jds. Finally, we generalize a well-known characterization for acyclic jds by proving that n-cyclicity is equivalent to “n-wise consistency implies global consistency.” As a consequence, consistency checking can be performed in polynomial time if we restrict ourselves to n-cyclic jds, for a tired value of n, not necessarily equal to 2.

A grammar-based approach towards unifying hierarchical data models

A simple model for representing the hierarchical structure of information is proposed. This model, called the grammatical model, is based on trees that are generated by grammars; the grammars describe the hierarchy of the information represented by the trees. Two transformation languages, an algebra and a calculus, are presented and shown to be equally expressive.

An Introduction to the Completeness of Languages for Complex Objects and Nested Relations

Languages for models of nested relations and complex objects have been attracting considerable attention recently. Some of these languages are algebraic, others are calculus based, some are logic programming oriented. This paper describes these languages and surveys recent results about the expressive power of these languages. The emphasis is on completeness issues. The expressive power of the languages is described in terms of the three common types of completeness: calculus-completeness, BP-completeness and CH-completeness.

A uniform approach toward handling atomic and structured information in the nested relational database model

The algebras and query languages for nested relations defined thus far do not allow us to “flatten” a relation scheme by disregarding the internal representation of data. In real life, however, the degree in which the structure of certain information, such as addresses, phone numbers, etc., is taken into account depends on the particular application and may even vary in time. Therefore, an algebra is proposed that does allow us to simplify relations by disregarding the internal structure of a certain class of information. This algebra is based on a careful manipulation of attribute names. Furthermore, the key operator in this algebra, called “copying,” allows us to deal with various other common queries in a very uniform manner, provided these queries are interpreted as operations on classes of semantically equivalent relations rather than individual relations. Finally, it is shown that the proposed algebra is complete in the sense of Bancilhon and Paredaens.

Object histories which avoid certain subsequences

Abstract In an earlier paper, one of the authors introduced a record-based model for describing historical data for objects (here called “object histories”). The major construct in the model is a computation-tuple sequence scheme (abbreviated CSS) which specifies the set of all “valid” object histories for the same type of object. In follow-up articles, the effects of interval queries and projections on object histories were examined. Now one of the components in a CSS is a finite set of constraints on object histories. In the present investigation the notion of bad-subsequence constraint is defined and CSS in which each constraint is of this kind are studied. (A bad-subsequence constraint σ is specified by a given set b of object histories. An object history u satisfies σ if u has no subsequence which is a sequence in b .) Among the results are the following: (i) Necessary and sufficient conditions for a set of object histories described by a given CSS to be described by another CSS having only bad-subsequence constraints, i.e., when a given CSS is bad-subsequence representable; (ii) a characterization for when a bad-subsequence-representable CSS is also locally representable (in the sense of one of the earlier papers); and (iii) connections of bad-subsequence representability with functional-dependency representability.

Another view of functional and multivalued dependencies in the relational database model

In this paper, pseudo-functional and pseudo-multivalued dependencies are introduced. They are shown to be isomorphic with functional and multivalued dependencies, i.e., they behave in the same way with respect to implication. This formalism leads in a very natural way to a rather efficient algorithm for the inference of functional and multivalued dependencies. Some applications to acyclic join dependencies are discussed.

On the decomposition of join dependencies

In [9] we proposed a method for decomposing join dependencies (jds) in a relational database. Decomposing a jd can be useful for separating cyclic and acyclic parts of jds, obtaining more insight in the structure of a jd or making integrity-checking more efficient. The decomposition methodology of [9] has many desirable properties. However, in general it cannot generate all the decompositions of a given jd. In this paper, we first recall this decomposition methodology and its most important properties. We then introduce a subclass of jds, the unambiguous jds. We show that this class represents exactly those jds that have a unique decomposition (which can be obtained by our method). We also give a characterization of this decomposition in terms of the structure of the original jd. To prove our results, we make extensive use of hypergraph theory.

The Nested Relational Database Model

Up to this point, we have been dealing with the standard relational model introduced by Codd. Probably, one of the most fundamental assumptions made in this model is that data is represented in the form of flat tables; this is the so called first normal form assumption. In many practical circumstances, however, data is not represented as flat tables but rather in the form of hierarchically organized tables. For example consider the table shown in Figure 7.1. A row in that table represents a person, the set of his or her natural children and for each child, the set of his or her toys. In the relational model this table would be represented as shown in Figure 7.2. The argument made by many people is that the hierarchically organized table is a more natural representation of this data. So there is a need to represent and manipulate such data.