Containment and Optimization of Object-Preserving Conjunctive Queries

Abstract

In the optimization of queries in an object-oriented database (OODB) system, a natural first step is to use the typing constraints imposed by the schema to transform a query into an equivalent one that logically accesses a minimal set of objects. We study a class of queries for OODBs called conjunctive queries. Variables in a conjunctive query range over heterogeneous sets of objects. Consequently, a conjunctive query is equivalent to a union of conjunctive queries of a special kind, called terminal conjunctive queries. Testing containment is a necessary step in solving the equivalence and minimization problems. We first characterize the containment and minimization conditions for the class of terminal conjunctive queries. We then characterize containment for the class of all conjunctive queries and derive an optimization algorithm for this class. The equivalent optimal query produced is expressed as a union of terminal conjunctive queries, which has the property that the number of variables as well as their search spaces are minimal among all unions of terminal conjunctive queries. Finally, we investigate the complexity of the containment problem. We show that it is complete in $\Pi^{p}_{2}$.