Query Unnesting in Object-Oriented Databases

There is already a sizable body of proposals on OODB query optimization. One of the most challenging problems in this area is query unnesting, where the embedded query can take any form, including aggregation and universal quantification. Although there is already a number of proposed techniques for query unnesting, most of these techniques are applicable to only few cases. We believe that the lack of a general and simple solution to the query unnesting problem is due to the lack of a uniform algebra that treats all operations (including aggregation and quantification) in the same way. This paper presents a new query unnesting algorithm that generalizes many unnesting techniques proposed recently in the literature. Our system is capable of removing any form of query nesting using a very simple and efficient algorithm. The simplicity of the system is due to the use of the monoid comprehension calculus as an intermediate form for OODB queries. The monoid comprehension calculus treats op..

Rewriting Declarative Query Languages

Queries against databases are formulated in declarative languages. Examples are the relational query language SQL and XPath or XQuery for querying data stored in XML. Using a declarative query language, the querist does not need to know about or decide on anything about the actual strategy a system uses to answer the query. Instead, the system can freely choose among the algorithms it employs to answer a query. Predominantly, query processing in the relational context is accomplished using a relational algebra. To this end, the query is translated into a logical algebra. The algebra consists of logical operators which facilitate the application of various optimization techniques. For example, logical algebra expressions can be rewritten in order to yield more efficient expressions. In order to query XML data, XPath and XQuery have been developed. Both are declarative query languages and, hence, can benefit from powerful optimizations. For instance, they could be evaluated using an algebraic framework. However, in general, the existing approaches are not directly utilizable for XML query processing. This thesis has two goals. The first goal is to overcome the above-mentioned misfits of XML query processing, making it ready for industrial-strength settings. Specifically, we develop an algebraic framework that is designed for the efficient evaluation of XPath and XQuery. To this end, we define an order-aware logical algebra and a translation of XPath into this algebra. Furthermore, based on the resulting algebraic expressions, we present rewrites in order to speed up the execution of such queries. The second goal is to investigate rewriting techniques in the relational context. To this end, we present rewrites based on algebraic equivalences that unnest nested SQL queries with disjunctions. Specifically, we present equivalences for unnesting algebraic expressions with bypass operators to handle disjunctive linking and correlation. Our approach can be applied to quantified table subqueries as well as scalar subqueries. For all our results, we present experiments that demonstrate the effectiveness of the developed approaches

An Algebraic Approach to XQuery Optimization

As more data is stored in XML and more applications need to process this data, XML query optimization becomes performance critical. While optimization techniques for relational databases have been developed over the last thirty years, the optimization of XML queries poses new challenges. Query optimizers for XQuery, the standard query language for XML data, need to consider both document order and sequence order. Nevertheless, algebraic optimization proved powerful in query optimizers in relational and object oriented databases. Thus, this dissertation presents an algebraic approach to XQuery optimization. In this thesis, an algebra over sequences is presented that allows for a simple translation of XQuery into this algebra. The formal definitions of the operators in this algebra allow us to reason formally about algebraic optimizations. This thesis leverages the power of this formalism when unnesting nested XQuery expressions. In almost all cases unnesting nested queries in XQuery reduces query execution times from hours to seconds or milliseconds. Moreover, this dissertation presents three basic algebraic patterns of nested queries. For every basic pattern a decision tree is developed to select the most effective unnesting equivalence for a given query. Query unnesting extends the search space that can be considered during cost-based optimization of XQuery. As a result, substantially more efficient query execution plans may be detected. This thesis presents two more important cases where the number of plan alternatives leads to substantially shorter query execution times: join ordering and reordering location steps in path expressions. Our algebraic framework detects cases where document order or sequence order is destroyed. However, state-of-the-art techniques for order optimization in cost-based query optimizers have efficient mechanisms to repair order in these cases. The results obtained for query unnesting and cost-based optimization of XQuery underline the need for an algebraic approach to XQuery optimization for efficient XML query processing. Moreover, they are applicable to optimization in relational databases where order semantics are considered