Efficient methods of processing unanticipated queries are a crucial prerequisite for the success of generalized database management systems. A wide variety of approaches to improve the performance of query evaluation algorithms have been proposed: logic-based and semantic transformations, fast implementations of basic operations, and combinatorial or heuristic algorithms for generating alternative access plans and choosing among them. These methods are presented in the framework of a general query evaluation procedure using the relational calculus representation of queries. In addition, nonstandard query optimization issues such as higher level query evaluation, query optimization in distributed databases, and use of database machines are addressed. The focus, however, is on query optimization in centralized database systems.

Strategy for processing multivariable queries in the database management system INGRES is considered. The general procedure is to decompose the query into a sequence of one-variable queries by alternating between (a) reduction: breaking off components of the query which are joined to it by a single variable, and (b) tuple substitution: substituting for one of the variables a tuple at a time. Algorithms for reduction and for choosing the variable to be substituted are given. In most cases the latter decision depends on estimation of costs; heuristic procedures for making such estimates are outlined.

Object-Relational database management systems allow knowledgeable users to de ne new data types, as well as new methods (operators) for the types. This exibility produces an attendant complexity, which must be handled in new ways for an Object-Relational database management system to be e cient. In this paper we study techniques for optimizing queries that contain time-consuming methods. The focus of traditional query optimizers has been on the choice of join methods and orders; selections have been handled by \pushdown " rules. These rules apply selections in an arbitrary order before as many joins as possible, using the assumption that selection takes no time. However, users of Object-Relational systems can embed complex methods in selections. Thus selections may take signi cant amounts of time, and the query optimization model must be enhanced. In this paper, we carefully de ne a query cost framework that incorporates both selectivity and cost estimates for selections. We develop an algorithm called Predicate Migration, and prove that it produces optimal plans for queries with expensive methods. We then describe our implementation of Predicate Migration in the commercial Object-Relational database management system Illustra, and discuss practical issues that a ect our earlier assumptions. We compare Predicate Migration to a variety of simpler optimization techniques, and demonstrate that Predicate Migration is the best general solution to date. The alternative techniques we presentmaybe useful for constrained workloads.

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