This thesis describes a new approach of relational database design using the SET conceptual model. The SET conceptual model is used for information modelling. The database schema generated from the information modelling is called the SET schema. The SET schema consists of the declarations of all the sets of the database schema. A domain graph can be constructed based on the information declared in the SET schema. A domain graph is a directed graph with nodes labelled with declared sets and arcs labelled with degree information. Each are in the domain graph points to a node S from a node labelled with an immediate domain predecessor of S. The new method of table design for the relational database involves partitioning the domain graph into mutually exclusive <1,1>-connected components based on the degree information. These components (subgraphs) are then transformed into tree structures. These trees are extended to include the domain predecessors of their nodes to make them predecessor total. The projections of these extended trees into the value sets labelling their leaf nodes form a set of relations which can be represented by tables. This table design method is described and presented in this thesis, along with d program that automates the method. Given a schema of the SET model, together with some degree information about defined sets that a user must calculate based on the intention of the defined sets, the program produces a relational database schema that will record data for the SET schema correctly and completely. / Science, Faculty of / Computer Science, Department of / Graduate

Approved for public release; distribution in unlimited. / The relational database model has become the most popular and widespread database model. Most current database systems are based upon or related to -he relational model. However, the relational model is beset with significant limitations, pitfalls and deficiencies. The relational model can be substantially improved with graphical interfaces. To this end, the Graphics Language for Accessing Database (GLAD) can provide easy to use and learn graphics interfaces for the relational model. Data structures and algorithms for GLAD will be presented to extend the relational model. / http://archive.org/details/datastructuresal00gren / Captain, United States Marine Corps

Yu Xiaohui. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 98-115). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Related Work --- p.6 / Chapter 2.1 --- Query Optimization --- p.6 / Chapter 2.2 --- Query Rewriting --- p.8 / Chapter 2.2.1 --- Optimizing Multi-Block Queries --- p.8 / Chapter 2.2.2 --- Semantic Query Optimization --- p.13 / Chapter 2.2.3 --- Query Rewriting in Starburst --- p.15 / Chapter 2.3 --- Plan Generation --- p.16 / Chapter 2.3.1 --- Dynamic Programming Approach --- p.16 / Chapter 2.3.2 --- Join Query Processing --- p.17 / Chapter 2.3.3 --- Queries with Aggregates --- p.23 / Chapter 2.4 --- Statistics and Cost Estimation --- p.24 / Chapter 2.5 --- Histogram Techniques --- p.27 / Chapter 2.5.1 --- Definitions --- p.28 / Chapter 2.5.2 --- Trivial Histograms --- p.29 / Chapter 2.5.3 --- Heuristic-based Histograms --- p.29 / Chapter 2.5.4 --- V-Optimal Histograms --- p.32 / Chapter 2.5.5 --- Wavelet-based Histograms --- p.35 / Chapter 2.5.6 --- Multidimensional Histograms --- p.35 / Chapter 2.5.7 --- Global Histograms --- p.37 / Chapter 3 --- New Histogram Techniques --- p.39 / Chapter 3.1 --- Piecewise Linear Histograms --- p.39 / Chapter 3.1.1 --- Construction --- p.41 / Chapter 3.1.2 --- Usage --- p.43 / Chapter 3.1.3 --- Error Measures --- p.43 / Chapter 3.1.4 --- Experiments --- p.45 / Chapter 3.1.5 --- Conclusion --- p.51 / Chapter 3.2 --- A-Optimal Histograms --- p.54 / Chapter 3.2.1 --- A-Optimal(mean) Histograms --- p.56 / Chapter 3.2.2 --- A-Optimal(median) Histograms --- p.58 / Chapter 3.2.3 --- A-Optimal(median-cf) Histograms --- p.59 / Chapter 3.2.4 --- Experiments --- p.60 / Chapter 4 --- Global Histograms --- p.64 / Chapter 4.1 --- Wavelet-based Global Histograms --- p.65 / Chapter 4.1.1 --- Wavelet-based Global Histograms I --- p.66 / Chapter 4.1.2 --- Wavelet-based Global Histograms II --- p.68 / Chapter 4.2 --- Piecewise Linear Global Histograms --- p.70 / Chapter 4.3 --- A-Optimal Global Histograms --- p.72 / Chapter 4.3.1 --- Experiments --- p.74 / Chapter 5 --- Dynamic Maintenance --- p.81 / Chapter 5.1 --- Problem Definition --- p.83 / Chapter 5.2 --- Refining Bucket Coefficients --- p.84 / Chapter 5.3 --- Restructuring --- p.86 / Chapter 5.4 --- Experiments --- p.91 / Chapter 6 --- Conclusions --- p.95 / Bibliography --- p.98

A materialized view is a derived data collecton stored in a database. When the source data for a materialized view is updated, the materialized view also needs to be updated. The process of updating a materialized view in response to changes in the source data is called view maintenance. There are two methods for maintaining a materialized view - recomputation and incremental computation. Recomputation computes the new view instance from scratch using the updated sources data. Incremental computation on the other hand, computes the new view instance by using the update to the source data, the old view instance, and possibly some source data. Incremental computation is widely accepted as a less expensive mathod of maintaining a view when the size of the update to the source data is small in relation to the size of the source data. / thesis (PhD)--University of South Australia, 2000

Ph.D. / Computer Science and Engineering / Join-order optimization plays a central role in the processing of relational database queries. This dissertation presents two new algorithms for join-order optimization: a deterministic, exhaustive-search algorithm, and a stochastic algorithm that is based on the deterministic one. The deterministic algorithm achieves new complexity bounds for exhaustive search in join-order optimization; and in timing tests, both algorithms are shown to run many times faster than their predecessors. In addition, these new, fast algorithms search a larger space of join orders than is customary in join-order optimization. Not only do they consider all the so-called bushy join orders, rather than just the left-deep ones, but-what is more unusual-they also consider all join orders that contain Cartesian products. The novel construction of these algorithms enables them to search a space including Cartesian products without paying the performance penalty that is conventionally associated with such a search.

Support of order in query processing is a crucial component in relational database systems, not only because the output of a query is often required to be sorted in a specific order, but also because employing order properties can significantly reduce the query execution cost. Therefore, finding an effective approach to answer queries over ordered data is important to the efficiency of query processing in relational databases. In this dissertation, an ordered relational database model is proposed, which captures both data tuples of relations and tuple ordering in relations. Based on this conceptual model, ordered relational queries are formally defined in a two-sorted first-order calculus, which serves as a yardstick to evaluate expressive power of other ordered query representations. The primary purpose of this dissertation is to investigate the expressive power of different ordered query representations. Particularly, the completeness problem of ordered relational algebras is studied with respect to the first-order calculus: does there exist an ordered algebra such that any first-order expressible ordered relational query can be expressed by a finite sequence of ordered operations? The significance of studying the completeness problem of ordered relational algebras is in that the completeness of ordered relational algebras leads to the possibility of implementing a finite set of ordered operators to express all first-order expressible ordered queries in relational databases. The dissertation then focuses on the completeness problem of ordered conjunctive queries. This investigation is performed in an incremental manner: first, the ordered conjunctive queries with data-decided order is considered; then, the ordered conjunctive queries with t-decided order is studied; finally, the completeness problem for the general ordered conjunctive queries is explored. The completeness theorem of ordered algebras is proven for all three classes of ordered conjunctive queries. Although this ordered relational database model is only conceptual, and ordered operators are not implemented in this dissertation, we do prove that a complete set of ordered operators exists to retrieve all first order expressible ordered queries in the three classes of ordered conjunctive queries. This research sheds light on the possibility of implementing a complete set of ordered operators in relational databases to solve the performance problem of order-relevant queries.

An early vision in Computer Science was to create intelligent systems ca- pable of reasoning on large amounts of data. Independent results in the areas of Description Logic and Relational Databases have advanced us towards this vision. Description Logic research has advanced the understanding of the tradeoff between the computational complexity of reasoning and the expressiveness of logic languages, and now underpins the Semantic Web. The Semantic Web comprises a graph data model (RDF), an ontology language for knowledge representation and reasoning (OWL) and a graph query language (SPARQL). Database research has advanced the theory and practice of management of data, embodying features such as views and recursion which are capable of representing reasoning. Despite the independent advances, the interface between Relational Databases and Semantic Web is poorly understood. This dissertation revisits this vision with respect to current technology and addresses the following question: How and to what extent can Relational Databases be integrated with the Semantic Web? The thesis is that much of the existing Relational Database infrastructure can be reused to support the Semantic Web. Two problems are studied. Can a Relational Database be automatically virtualized as a Semantic Web data source? This paradigm comprises a single Relational Database. The first contribution is an automatic direct mapping from a Relational Database schema and data to RDF and OWL. The second contribution is a method capable of evalu- ating SPARQL queries against the Relational Database, per the direct mapping, by exploiting two existing relational query optimizations. These contributions are embodied in a system called Ultrawrap. Empirical analysis consistently yield that SPARQL query execution performance on Ultrawrap is comparable to that of SQL queries written directly for the relational representation of the data. Such results have not been previously achieved. Can a Relational Database be mapped to existing Semantic Web ontologies and act as a reasoner? This paradigm comprises an OWL ontology including inheritance and transitivity, a Relational Database and mappings between the two. A third contribution is a method for Relational Databases to support inheritance and transitivity by compiling the ontology as mappings, implementing the mappings as SQL views, using SQL recursion and optimizing by materializing a subset of views. This contribution is implemented in an extension of Ultrawrap. Empirical analysis reveals that Relational Databases are able to effectively act as reasoners. / text

In relational algebra, a recursive relation R is defined by an equation of the form R = f(R), where f(R) is a positive relational algebra expression. Such an equation can be solved by applying a general closure operator. Although some optimization is possible, the performance obtained using this approach is very dependent on the form of the equation which defines R. Principally for this reason, we have developed specialized closure operators for relations which are solutions to problems of practical importance such as transitive closure, accessibility, shortest path, bill-of-materials, and deductions by containment comparisons. / This approach has led to the following general results: (1) design, classification, and analysis of many iterative methods for evaluating recursive relations, as well as analysis of experimental results; (2) formalization of the concept of iterative evaluation of a relation; (3) demonstration that domain algebra can be used to solve problems of concatenation and aggregation of the information associated with a recursive structure; (4) proof that relational division and general containment joins are left-monotone. / More specific results consist of a collection of original algorithms which run well on secondary storage, as shown by simulations. Among them, we wish to emphasize the differencing logarithmic transitive closure (TC) algorithms, which are superior to the previously known relational TC algorithms, and the shortest path algorithms, which are in fact generic algorithms for path algebra problems.

Support of order in query processing is a crucial component in relational database systems, not only because the output of a query is often required to be sorted in a specific order, but also because employing order properties can significantly reduce the query execution cost. Therefore, finding an effective approach to answer queries over ordered data is important to the efficiency of query processing in relational databases. In this dissertation, an ordered relational database model is proposed, which captures both data tuples of relations and tuple ordering in relations. Based on this conceptual model, ordered relational queries are formally defined in a two-sorted first-order calculus, which serves as a yardstick to evaluate expressive power of other ordered query representations. The primary purpose of this dissertation is to investigate the expressive power of different ordered query representations. Particularly, the completeness problem of ordered relational algebras is studied with respect to the first-order calculus: does there exist an ordered algebra such that any first-order expressible ordered relational query can be expressed by a finite sequence of ordered operations? The significance of studying the completeness problem of ordered relational algebras is in that the completeness of ordered relational algebras leads to the possibility of implementing a finite set of ordered operators to express all first-order expressible ordered queries in relational databases. The dissertation then focuses on the completeness problem of ordered conjunctive queries. This investigation is performed in an incremental manner: first, the ordered conjunctive queries with data-decided order is considered; then, the ordered conjunctive queries with t-decided order is studied; finally, the completeness problem for the general ordered conjunctive queries is explored. The completeness theorem of ordered algebras is proven for all three classes of ordered conjunctive queries. Although this ordered relational database model is only conceptual, and ordered operators are not implemented in this dissertation, we do prove that a complete set of ordered operators exists to retrieve all first order expressible ordered queries in the three classes of ordered conjunctive queries. This research sheds light on the possibility of implementing a complete set of ordered operators in relational databases to solve the performance problem of order-relevant queries.

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