Rule-based optimization and query processing in an extensible geometric database system

Abstract

Gral is an extensible database system, based on the formal concept of a many-sorted relational algebra. Many-sorted algebra is used to define any application's query language, its query execution language, and its optimization rules. In this paper we describe Gral's optimization component. It provides (1) a sophisticated rule language-rules are transformations of abstract algebra expressions, (2) a general optimization framework under which more specific optimization algorithms can be implemented, and (3) several control mechanisms for the application of rules. An optimization algorithm can be specified as a series of steps Each step is defined by its own collection of rules together with a selected control strategy. The general facilities are illustrated by the complete design of an example optimizer-in the form of a rule file-for a small nonstandard query language and an associated execution language. The query language includes selection, join, ordering, embedding derived values, aggregate functions, and several geometric operations. The example shows in particular how the special processing techniques of a geometric database system, such as spatial join methods and geometric index structures, can be integrated into query processing and optimization of a relational database system. A similar, though larger, optimizer is fully functional within the geometric database system implemented as a Gral prototype.

Query evaluation techniques for large databases

“…Interestingly, B-trees seem to be having a renaissance as a research subject, in particular with respect to improved space utilization [Baeza-Yates and Larson 1989] While most current database system implementations only use some form of B-trees, an amazing variety of index structures has been described in the literature, e.g., [Becker, Six, and Widmayer 1991;Beckmann et al 1990;Bentley 1975;Finkel and Bentley 1974;Guenther and Bilmes 1991;Gunther and Wong 1987;Gunther 1989;Guttman 1984;Henrich, Six, and Widmayer 1989;Hoel and Samet 1992;Hutflesz, Six, and Widmayer 1988a;Hutflesz, Six, and Widmayer 1988b;Hutflesz, Six, and Widmayer 1990;Jagadish 1991;Kemper and Wallrath 1987;Kolovson and Stonebraker 1991;Kriegel and Seeger 1987;Kriegel and Seeger 1988;Lomet and Salzberg 1990b;Lomet 1992;Neugebauer 1991;Robinson 1981;Samet 1984;. One of the few multi-dimensional index structures actually implemented in a complete database management system are R-trees in Postgres [Guttman 1984;Stonebraker, Rowe, and Hirohama 1990].…”

Implementation of the ROSE algebra: Efficient algorithms for realm-based spatial data types

“…We are currently working on the definition and implementation of a general "algebra interface" between an external implementation of a system of data types and a database system. The ROSE algebra will be made available under such an interface and integrated into the Gral system [Gü89,BeG92]. In this approach, it is only necessary to replace the array components "at the end" of object representations by identifiers of so-called "database arrays" which behave exactly like ordinary arrays but have their own page sequences and buffer management and interact properly with DBMS transaction management.…”

“…To be precise, we must distinguish between a descriptive and an executable algebra [Gü89,BeG92]. A descriptive algebra offers types and operations at a conceptual level which can be used to formulate queries; its semantics are given by defining a "carrier" set of objects for each sort of the algebra and a function for each operator.…”

Experience with SAND-Tcl: A Scripting Tool for Spatial Databases

“…A walkthrough of the script given above will help to make these concepts clear: 3 The choice of which spatial index should be used is done by means of a command which is not explained here since it is not relevant to our discussion. It suffices to say that both structures provide exactly the same functionality.…”

“…Query optimizers (e.g., [3,11,21]) are prime examples of programs which generate other programs. The ultimate goal of a query optimizer is to produce a program that evaluates a given query in the most efficient manner.…”