Wai Yin Mok

A normal form for precisely characterizing redundancy in nested relations

We give a straightforward definition for redundancy in individual nested relations and define a new normal form that precisely characterizes redundancy for nested relations. We base our definition of redundancy on an arbitrary set of functional and multivalued dependencies, and show that our definition of nested normal form generalizes standard relational normalization theory. In addition, we give a condition that can prevent an unwanted structural anomaly in nested relations, namely, embedded nested relations with at most one tuple. Like other normal forms, our nested normal form can serve as a guide for database design.

A comparative study of various nested normal forms

As object-relational databases (ORDBs) become popular in the industry, it is important for database designers to produce database schemes with good properties in these new kinds of databases. One distinguishing feature of an ORDB is that its tables may not be in first normal form. Hence, ORDBs may contain nested relations along with other collection types. To help the design process of an ORDB, several normal forms for nested relations have recently been defined, and some of them are called nested normal forms. In this paper, we investigate four nested normal forms, which are NNF [20], NNF [21], NNF [23], and NNF [25], with respect to generalizing 4NF and BCNF, reducing redundant data values, and design flexibility. Another major contribution of this paper is that we provide an improved algorithm that generates nested relation schemes in NNF [20] from an a-acyclic database scheme, which is the most general type of acyclic database schemes. After presenting the algorithm for NNF [20], the algorithms of all of the four nested normal forms and the nested database schemes that they generate are compared. We discovered that when the given set of MVDs is not conflict-free, NNF [20] is inferior to the other three nested normal forms in reducing redundant data values. However, in all of the other cases considered in this paper, NNF [20] is at least as good as all of the other three nested normal forms.

Generating compact redundancy-free XML documents from conceptual-model hypergraphs

As XML data becomes more and more prevalent and as larger quantities of data find their way into XML documents, the need for quality XML data organization only increase. One standard way of structuring data well is to reduce and, if possible, eliminate redundancy, while at the same time making the storage structures as compact as possible. In this paper, we present a methodology to generate XML storage structures where conforming XML documents are redundancy-free, and for most practical cases, are also fully compact. Our methodology assumes the input is a conceptual-model hypergraph. For the special case that every edge in the hypergraph is binary, we present a simple algorithm, guaranteed to always generate redundancy-free storage structures. We show, however, that generating a minimum number of redundancy-free storage structures is NP-hard. We therefore provide heuristics to guide the process and observe that these heuristics result in satisfactory solutions, which are often optimal. We then present a general algorithm for n-ary edges and show that it generates redundancy-free storage structures. The general algorithm must overcome several problems that do not arise in the special case

Transforming Conceptual Models to Object-Oriented Database Designs: Practicalities, Properties, and Peculiarities

More work is needed on devising practical, but theoretically well-founded procedures for doing object-oriented database (OODB) design. Besides being practical and having formal properties, these design procedures should also be flexible enough to allow for peculiarities that make applications unique. In this paper, we present and discuss an OODB design procedure that addresses these problems. The procedure we discuss is practical in the sense that it is based on a common family of conceptual models and in the sense that it does not expect users to supply esoteric, difficult-to-discover, and hard-to-understand constraints (such as multivalued dependencies), nor does it make hard-to-check and easy-to-overlook assumptions (such as the universal relation assumption). At the same time, the procedure is well-founded and formal, being based on a new theoretical result that characterizes properties of interest in designing complex objects. It is also flexible and adaptable to the peculiarities of a wide variety of applications.

Mapping Conceptual Models to Database Schemas

From the beginning, a primary objective of conceptual modeling has been to generate good database schemas. This chapter surveys and explains the principles and practices of algorithmically mapping conceptual models to database schemas. An important unifying theme is that the underlying principles are independent of conceptual-modeling languages and notation. Although illustrated mainly in terms of the entity-relationship model, the chapter explains and illustrates the application of the mapping principles to extended entity-relationship models, the unified modeling language, and generic conceptual-model hypergraphs. Besides explaining conceptual-model-independent mapping rules, the chapter also addresses normalization issues, explaining both the map-then-normalize approach and the normalize-then-map approach to schema normalization. In addition to mapping conceptual models to flat relations for standard relational databases, the chapter also shows how to map conceptual models to nested relations applicable for object-based and XML storage structures.

Extracting a largest redundancy-free XML storage structure from an acyclic hypergraph in polynomial time

Given a hypergraph and a set of embedded functional dependencies, we investigate the problem of determining the conditions under which we can efficiently generate redundancy-free XML storage structures with as few scheme trees as possible. Redundancy-free XML structures guarantee both economy in storage space and the absence of update anomalies, and having the least number of scheme trees requires the fewest number of joins to navigate among the data elements. We know that the general problem is intractable. The problem may still be intractable even when the hypergraph is acyclic and each hyperedge is in Boyce-Codd normal form (BCNF). As we show here, however, given an acyclic hypergraph with each hyperedge in BCNF, a polynomial-time algorithm exists that generates a largest possible redundancy-free XML storage structure. Successively generating largest possible scheme trees from among hyperedges not already included in generated scheme trees constitutes a reasonable heuristic for finding the fewest possible scheme trees. For many practical cases, this heuristic finds the set of redundancy-free XML storage structures with the fewest number of scheme trees. In addition to a correctness proof and a complexity analysis showing that the algorithm is polynomial, we also give experimental results over randomly generated but appropriately constrained hypergraphs showing empirically that the algorithm is indeed polynomial.

On the computability of agent-based workflows

Workflow research is commonly concerned with optimization, modeling, and dependency. In this research, we however address a more fundamental issue. By modeling humans and machines as agents and making use of a theoretical computer and statecharts, we prove that many workflow problems do not have computer-based solutions. We also demonstrate a sufficient condition under which computers are able to solve these problems. We end by discussing the relationships between our research and Petri Nets, the multi-agent framework in the literature, linear programming and workflow verification.

Using Harel's Statecharts to Model Business Workflows

In this paper, we model business workflows using Harel’s statecharts. Mapping to statecharts allows us to systematically identify potential workflow problems. It also allows us to investigate specific properties inherent in actual business workflows. Our research focuses on three desirable properties of active database systems — termination, confluence, and observable determinism. For termination and confluence, we develop algorithms to provide a theoretical lens linking desirable active database system properties to workflow management systems problems. We initially validate our algorithms by mapping business workflows from a case study. Our research thus builds preliminary theory by developing a systematic method for identifying workflow problems.

Using NNF to transform conceptual data models to object-oriented database designs

More work is needed on devising practical, but theoretically well-founded procedures for doing object-oriented database (OODB) design [17]. Design procedures should also be flexible enough to take into account various application characteristics (such as whether objects are very large or are read-only). In this paper, we present and discuss an OODB design procedure that addresses these problems. The procedure is practical in the sense that it is based on a common family of conceptual models and in the sense that it does not expect users to supply esoteric, difficult-to-discover, and hard-to-understand constraints (such as multivalued dependencies), nor does it make hard-to-check and easy-to-overlook assumptions (such as the universal relation scheme assumption). At the same time, the procedure is well-founded and formal, being based on NNF (Nested Normal Form [21]), a new theoretical result that characterizes properties of interest in designing complex objects. It is also adaptable to various applications characteristics.

Designing nesting structures of user-defined types in object-relational databases

This paper presents a methodology for designing proper nesting structures of user-defined types in object-relational databases. Briefly, we envision that users model a real-world application by using the EER model, which results in an EER schema. Our algorithm then uses the theory we developed for nested relations to generate scheme trees from the EER schema. We shall prove that the resulting scheme trees have exactly the same information content as the EER schema, and the scheme-tree instances over the resulting scheme trees do not store information redundantly. Finally, the scheme trees are transformed to Oracle Database 10g nested object types for implementation. The algorithm in this paper forms the core of a computerized object-relational database design tool we shall develop in the future.