Algebraic Equivalences Among Nested Relational Expressions

: Algebraic optimization are both theoretically and practically important for query processing in (nested) relational databases. In this paper, we consider this issue and investigate some algebraic properties concerning to the nested relational operators. We also outline a heuristic optimization algorithm for nested relational expressions by adopting algebraic transformation rules developed in this paper and previous related work. 1 Introduction In the last decade, much research has been carried out on nested relations and complex objects. By relaxing the 1NF assumption, the resulting nested relational model (sometimes called NF 2 ) can support such new applications as office automation, multimedia system, scientific data processing system, engineering design system, and so forth. In order to model these applications we use hierarchical structures rather than flat tables to enable the representation of complex objects. The nested relational model is the basis for bridging the rela..

Query translation and optimisation for complex value databases

This thesis considers the theory of database queries on the complex value data model extended with external functions. In modern intelligent database systems, we expect that query systems be able to handle a wide range of calculus formulas correctly and efficiently. Accordingly, they will require general query translators and efficient optimisers. Motivated by these concerns, this thesis undertakes a· comprehensive study of query evaluation in the complex value model and investigates the following issues: • identifying recursive sets of complex value formulas which define domain independent queries; • implementing complex value calculus queries with the incorporation of functions; • solving the problem of how to process join operation in complex value databases; and • investigating some algebraic properties concerning nested relational operators. The first part of this thesis extends some classical properties of the relational theory - particularly those related to query safety - to the context of complex value databases with fixed external functions and investigates the problem of how to implement calculus queries. Two notions of syntactic criteria for queries which guarantee domain independence, namely, embedded evaluable and embedded allowed, are generalised for this data model. This thesis shows that all embedded-allowed calculus (or fix-point) queries are external-function domain independent and continuous. This thesis discusses the topic of "embedded allowed database programs" and proves that embedded allowed stratified programs satisfying certain constraints are embedded domain independent. It also develops an algorithm for translating embedded allowed queries into equivalent algebraic expressions as a basis for evaluating safe queries in all calculus-based query classes. The second part of this thesis considers the issue of query optimisation for nested relational databases. Within a restricted set of nested schema trees, a join operator, called P-join, is proposed. The P-join operator does not require as many restructuring operators and combines the advantages of the extended natural join and recursive join for efficient data access. A P-join algorithm which takes advantage of a decomposed storage model and various join techniques available in the standard relational model to reduce the cost of join operation in nested relational databases is also proposed. Finally, this thesis investigates some algebraic properties of nested relational operators which are useful for query optimisation in the nested relational model and outlines a heuristic optimisation algorithm for nested relational expressions by adopting algebraic transformation rules developed in this thesis and previous related work

Formal extension of the relational model for the management of spatial and spatio-temporal data

[Resumen] En los últioms años, se ha realizado un gran esfuerzo investigador en la manipulación de datos especiales y Sistemas de Información Geográfica (SIG). Una clara limitación de las primeras aproximaciones es la falta de integración entre datos geográficos y alfanuméricos. Para resolver esto surge el área de Bases de Datos Espaciales. Los problemas que aparecen en este campo son muchos y complejos. Un primer ejemplo son las peculiaridades de las operaciones espaciales, como el calculo de la intersección espacial de dos superficies. Otro ejemplo es el elegir las estructuras de datos apropiadas (relaciones, capas, etc.) y el conjunto de operaciones adeucado. La combinación con las Bases de Datos Temporales da lugar a las Bases de Datos Espacio-temporales, en las que la inclusión de la dimensión temporal complica más los problemas anteriores. A pesar de la gran cantidad de aproximaciones propuestas, no se ha llegado todavía a una solución satisfactoria. La presente tesis propone una nueva solución que resuelve todos los problemas de modelado de datos espaciales y espacio-temporales resaltados arriba. Parte del trabajo se completó durante el proyecto ""CHOROCRONOS"": A Research Network for Saptiotemporal Database Systems"", financiado por la Unión Europea. El modelo propuesto en la tesis define tres tipos de dato punto, línea y superficie, que encajan perfectamente en la percepción humana. La definición de estos tipos de dato se basa en la definición previa de Quanta Espacial. Las estructuras de datos usadas son las relaciones no anidadas de modelo relacional puro. El conjunto de operaciones relacionales permite alcanzar casi por completo la funcionalidad propuesta en otros modelos. Todas las operaciones han sido definidas en base a un núcleo reducido de operaciones primitvas. Todos los tipos de datos, espaciales, espacio-temporales y convencionales se manipulan de forma uniforme con este conjunto de operaciones