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Normal forms that guide the process of database schema design have several key goals such as elimination of redundancies and preservation of integrity constraints, such as functional dependencies. It has long been known that complete elimination of redundancies and complete preservation of constraints cannot be achieved simultaneously. In this article, we use a recently introduced information-theoretic framework, and provide a quantitative analysis of the redundancy/integrity preservation trade-off, and give techniques for comparing different schema designs in terms of the amount of redundancy they carry. The main notion of the information-theoretic framework is that of an information content of each datum in an instance (which is a number in [0, 1]): the closer to 1, the less redundancy it carries. We start by providing a combinatorial criterion that lets us calculate, for a relational schema with functional dependencies, the lowest information content in its instances. This indicates how good the schema design is in terms of allowing redundant information. We then study the normal form 3NF, which tolerates some redundancy to guarantee preservation of functional dependencies. The main result provides a formal justification for normal form 3NF by showing that this normal form pays the smallest possible price, in terms of redundancy, for achieving dependency preservation. We also give techniques for quantitative comparison of different normal forms based on the redundancy they tolerate. Categories and Subject Descriptors: H.2.1 [Database Management]: Logical Design--Normal forms; schema and subschema; H.1.1 [Models and Principles]: Systems and Information Theory--Information theory; value of information General Terms: Design, Management, Theory Additional Key Words and Phrases: Database design, functional dependency, redundancy, Third Normal Form (3NF) ACM Reference Format: Kolahi, S. and Libkin, L. 2010. An information-theoretic analysis of worst-case redundancy in database design. ACM Trans. Datab. Syst, 35, 1, Article. 5 (February 2010), 32 pages. DOI = 10.1145/1670243.1670248 http://doi.acm.org/10.1145/1670243.1670248

This article takes a first step towards the design and normalization theory for XML documents. We show that, like relational databases, XML documents may contain redundant information, and may be prone to update anomalies. Furthermore, such problems are caused by certain functional dependencies among paths in the document. Our goal is to find a way of converting an arbitrary DTD into a well-designed one, that avoids these problems. We first introduce the concept of a functional dependency for XML, and define its semantics via a relational representation of XML We then define an XML normal form, XNF, that avoids update anomalies and redundancies. We study its properties, and show that XNF generalizes BCNF; we also discuss the relationship between XNF and normal forms for nested relations. Finally, we present a lossless algorithm for converting any DTD into one in XNF. General Terms: Design, Management, Theory Additional Key Words and Phrases: XML data, DTDs, design, normal form, functional dependencies

The authors characterize the relationship between different notions of locality for first-order logic. Varied conceptions are used to derive expressibility bounds that apply beyond the first-order case.

Graph databases have received much attention as of late due to numerous applications in which data is naturally viewed as a graph; these include social networks, RDF and the Semantic Web, biological databases, and many others. There are many proposals for query languages for graph databases that mainly fall into two categories. One views graphs as a particular kind of relational data and uses traditional relational mechanisms for querying. The other concentrates on querying the topology of the graph. These approaches, however, lack the ability to combine data and topology, which would allow queries asking how data changes along paths and patterns enveloping it. In this article, we present a comprehensive study of languages that enable such combination of data and topology querying. These languages come in two flavors. The first follows the standard approach of path queries, which specify how labels of edges change along a path, but now we extend them with ways of specifying how both labels and data change. From the complexity point of view, the right type of formalisms are subclasses of register automata. These, however, are not well suited for querying. To overcome this, we develop several types of extended regular expressions to specify paths with data and study their querying power and complexity. The second approach adopts the popular XML language XPath and extends it from XML documents to graphs. Depending on the exact set of allowed features, we have a family of languages, and our study shows that it includes efficient and highly expressive formalisms for querying both the structure of the data and the data itself. [ABSTRACT FROM AUTHOR]

In [1], Qian and Wiederhold presented an algorithm for the incremental recomputation of relational algebra expressions that was claimed to preserve a certain minimality condition. This condition guarantees that the incremental change sets do not contain any unnecessary tuples; so, redundant computations are not performed. We show that, in fact, their algorithm violates this condition. We present an improved algorithm that does preserve this notion of minimality. Index Terms - Relational algebra, incremental recomputation, change propagation, view maintenance.