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.
The join of two or even more multuiimensionalfiles has been discussed in detail for the binary equijoin. We propose an algorithm for the eficient evaluation of generaljoins on gruifiles. Since the implementation of the directory and the scales of the gridfile has been left open in the original grid file concept, we first discuss these issues und present the new BR2-directory representation. The grdfile can also be used to store geometric objects by trunsforming these objects into higher-dimensional points. Our algorithm also handles geometric joins on such data sets. We have developed a cost model to analyze the performance of our join algorithm. We present results concerning the binary equijoin and a special geometric join in this paper.
Abstract. We present a framework for representing the trajectories of moving objects and the time-varying results of operations on moving objects. This framework supports the realization of discrete data models of moving objects databases, which incorporate representations of moving objects based on non-linear approximation functions.
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