Containment and minimization of positive conjunctive queries in OODB's

With the availability of high-level declarative query languages in an object-oriented database system (OODB), the burden of choosing an efficient execution plan for a query is transferred from the user to the database 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 propose a class of queries called conjunctive queries for OODB's. A conjunctive query can be expressed as an equivalent union of queries in a special form called terminal conjunctive queries. We first characterize the containment, and hence equivalence, conditions for the class of terminal conjunctive queries. We then study a subclass of conjunctive queries called positive conjunctive queries. We characterize the containment and equivalence conditions, as well as derive an algorithm for finding an exact minimization for the class of positive conjunctive queries. The equivalent minimized query is expressed as a union of terminal positive conjunctive queries with the property that the variable search space is minimal among all the unions of postivie conjunctive queries.