Millist W. Vincent

Strong functional dependencies and their application to normal forms in XML

In this article, we address the problem of how to extend the definition of functional dependencies (FDs) in incomplete relations to XML documents (called XFDs) using the well-known strong satisfaction approach.We propose a syntactic definition of strong XFD satisfaction in an XML document and then justify it by showing that, similar to the case in relational databases, for the case of simple paths, keys in XML are a special case of XFDs. We also propose a normal form for XML documents based on our definition of XFDs and provide a formal justification for it by proving that it is a necessary and sufficient condition for the elimination of redundancy in an XML document.

Functional dependencies for XML

In this paper we address the problem of how to extend the definition of functional dependencies (FDs) in incomplete relations to XML documents. An incomplete relation is said to strongly satisfy a FD if every completion of the relation, obtained by replacing all null values by data values, satisfies the FD in the ordinary sense. We propose a syntactic definition of strong FD satisfaction in a XML document (called a XFD) and then justify it by proving that for a very general class of mappings of a relation into a XML document, a relation strongly satisfies a unary FD if and only if the XML document also strongly satisfies the equivalent XFD.

Semantic foundations of 4NF in relational database design

Abstract. The issue of providing a formal justification for the use of fourth normal form (4NF) in relational database design is investigated. The motivation and formal definitions for three goals of database design are presented. These goals are the elimination of: redundancy, key-based update anomalies and fact-based replacement anomalies. It is then shown that, depending on the type of constraints permitted, either Boyce-Codd normal form (BCNF) or 4NF are the exact conditions needed to ensure most of the design goals. However, it is also shown that the conditions required to ensure the absence of a particular class of key-based update anomaly are new normal forms which have not previously been identified. In particular, for the case where the only constraints are functional dependencies (FDs), it is shown that the required normal form is a new normal form that is stronger than third normal form (3NF) yet weaker than BCNF. Similarly, in the more general case where both FD and multivalued dependencies (MVDs) are present, the required normal form is a new normal form that is weaker than 4NF.

Constraint Preserving Transformation from Relational Schema to XML Schema

XML has become the standard for publishing and exchanging data on the Web. However, most business data is managed and will remain to be managed by relational database management systems. As such, there is an increasing need to efficiently and accurately publish relational data as XML documents for Internet-based applications. One way to publish relational data is to provide virtual XML documents for relational data via an XML schema which is transformed from the underlying relational database schema such that users can access the relational database through the XML schema. In this paper, we discuss issues in transforming a relational database schema into the corresponding XML schema. We aim to preserve all integrity constraints defined in a relational database schema, to achieve high level of nesting and to avoid introducing data redundancy in the transformed XML schema. In the paper, we first propose a basic transformation algorithm which introduces no data redundancy, then we improve the algorithm by exploring further nesting of the transformed XML schema.

Multivalued dependencies and a 4NF for XML

While providing syntactic flexibility, XML provides little semantic content and so the study of integrity constraints in XML plays an important role in helping to improve the semantic expressiveness of XML. Functional dependencies (FDs) and multivalued dependencies (MVDs) play a fundamental role in relational databases where they provide semantics for the data and at the same time are the foundation for database design. Since XML documents are closely coupled with relational databases in that XML documents are typically exported and imported from relational databases, the study of FDs and MVDs in XML is of fundamental significance in XML research. In this paper we define multivalued dependencies in XML (XMVDs). We then propose a normal form for XML documents in the presence of XMVDs and justify our normal form by showing that it ensures the elimination of redundancy.

Multivalued dependencies in XML

Functional dependencies (FDs) and multivalued dependencies (MVDs) play a fundamental role in relational databases where they provide semantics for the data and at the same time are the foundation for database design. Since XML documents are closely coupled with relational databases in that XML documents are typically exported and imported from relational databases, the study of FDs and MVDs in XML is of fundamental significance in XML research. In this paper we investigate the issue of defining multivalued dependencies in XML, a topic which to the best of our knowledge has not been previously investigated. We define multivalued dependencies in XML (XMVDs) and justify our definition by proving that, for a very general class of mappings from relations to XML, a relation satisfies an MVD if and only if the corresponding XML document satisfies the corresponding XMVD. Thus our definition of a XMVD in a XML document is a natural extension of the definition of a MVD in relations.

A Redundancy Free 4NF for XML

While providing syntactic flexibility, XML provides little semantic content and so the study of integrity constraints in XML plays an important role in helping to improve the semantic expressiveness of XML. Functional dependencies (FDs) and multivalued dependencies (MVDs) play a fundamental role in relational databases where they provide semantics for the data and at the same time are the foundation for database design. In some previous work, we defined the notion of multivalued dependencies in XML (called XMVDs) and defined a normal form for a restricted class of XMVDs, called hierarchical XMVDs. In this paper we generalise this previous work and define a normal form for arbitrary XMVDs. We then justify our definition by proving that it guarantees the elimination of redundancy in XML documents.

On the equivalence between FDs in XML and FDs in relations

With the growing use of the eXtensible Markup Language (XML) in database technology as a format for the permanent storage of data, the topic functional dependencies in XML (XFDs) has assumed increased importance because of its central role in database design. Recently, two different approaches have been proposed for defining an XFD. The first uses the concept of a ‘tree tuple’, whereas the second uses the concept of a ‘closest node’. In general, the two approaches are not comparable, but are comparable when a Document Type Definition is present and there is no missing information in the XML document. The first contribution of this article shows that when the two XFD definitions are comparable, the definitions are equivalent, and so there is essentially a common definition of an XFD in complete XML documents. The second contribution is to provide justification for the definition of a ‘closest node’ XFD. We show that if a complete flat relation is mapped to an XML document by an arbitrary sequence of nest operations, the XML document satisfies a ‘closest node’ XFD if and only if the relation satisfies the corresponding functional dependency. The class of XML documents generated in this fashion is a subset of the class of XML documents for which the two definitions of XFDs coincide. Hence ‘tree tuple’ and ‘closest node’ XFDs both capture the semantics of FDs when a complete relation is mapped to an XML document via arbitrary nesting.

Local XML functional dependencies

Keys and functional dependencies play a fundamental role in relational databases where they are used in integrity enforcement and in database design. Similarly, these constraints will play a fundamental role in XML and recently keys and functional dependencies in XML have been defined. In this paper we extend the previous definition of functional dependencies in XML to local functional dependencies in XML. Local functional dependencies (LFDs) are functional dependencies which hold only in a certain part of an XML document and not in the whole document. We also define, and prove correct, axioms for reasoning about the implication of LFDs in XML. Finally, we examine the relationship between LFDs and keys and show that the recently introduced concept of a relative key is a special case of a LFD.

Functional Dependencies, from Relational to XML

The flexibility of XML allows the same data to be represented in many different ways. Some representations may be better than others in that they require less storage or have less redundancy. In this paper we define functional dependencies in XML (XFDs) and investigate their effect on the design of XML documents. We then define two subtypes of XFDs, namely partial and transitive XFDs, which cause the same problems in XML document design as the corresponding types of FDs in relations. We further show that the removal of such types of XFDs can lead to a better document design. On the basis of this, we define the concept of upward XFDs and analyze its use in maximizing the nesting levels in XML documents without introducing redundancy. We further propose guidelines to nesting elements in XML documents.