Algebraic identities and query optimization in a parametric model for relational temporal databases

Abstract

This paper presents algebraic identities and algebraic query optimization for a parametric model for temporal databases. The parametric model has several features not present in the classical model. In this model a key is explicitly designated with a relation and an operator is available to change the key. The algebra for the parametric model is three-sorted; it includes relational expressions that evaluate to relations, domain expressions that evaluate to time domains, and boolean expressions that evaluate to TRUE or FALSE. The identities in the parametric model are classified as weak identities and strong identities. Weak identities in this model are largely counterparts of the identities in classical relational databases. Rather than establishing weak identities from scratch, a meta inference mechanism, introduced in the paper, allows weak identities to be induced from their classical counterpart. On the other hand, the strong identities will be established from scratch. An algorithm for algebraic optimization to transform a query to an equivalent query that will execute more efficiently is presented. Abstract. This paper presents algebraic identities and algebraic query optimization for a parametric model for temporal databases. The parametric model has several features not present in the classical model. In this model a key is explicitly designated with a relation and an operator is available to change the key. The algebra for the parametric model is three-sorted; it includes relational expressions that evaluate to relations, domain expressions that evaluate to time domains, and boolean expressions that evaluate to TRUE or FALSE. Disciplines Databases and Information Systems | Systems ArchitectureThe identities in the parametric model are classified as weak identities and strong identities. Weak identities in this model are largely counterparts of the identities in classical relational databases. Rather than establishing weak identities from scratch, a meta inference mechanism, introduced in the paper, allows weak identities to be induced from their classical counterpart. On the other hand, the strong identities will be established from scratch. An algorithm for algebraic optimization to transform a query to an equivalent query that will execute more efficiently is presented.

Spatio-temporal predicates

“…From this perspective, attribute timestamped models have the potential to fit very well with our purposes. Examples of temporal models integrating spatial aspects include variants of Gadia's temporal model [24], which are described in [6], [5]. A third approach has been to use linear constraints for modeling spatio-temporal data [27].…”

“…Another approach has been to appropriately extend a temporal data model based on attribute timestamps by spatial concepts. In contrast to tuple timestamped models, attribute time-stamped models (described in [8], [9], [24], [34], for example) aim at gathering information about an object in one tuple and allow complex attribute values. These complex values incorporate the temporal dimension and are frequently modeled as functions from time into a value domain, a view which is quite similar to ours.…”

A foundation for conventional and temporal query optimization addressing duplicates and ordering

“…The recent work of Gadia and Nair [13] considers query optimization for a parametric model for temporal databases, presents algebraic identities, and gives a heuristic optimization algorithm. They define a relation as a set of tuples, but they also consider weakly equivalent relations, i.e., relations that have the same snapshots.…”

An XML-based implementation of the parametric model for ad-hoc query of temporal and spatiotemporal data

“…In this section, we will discuss the simplified BNF (Backus Naur Form) of the three expressions, ParaSQL's user-friendliness, and some ParaSQL examples. An algebra leading to semantics of ParaSQL in terms of the relational operations is given in [19].…”