Practical Reformulation of Deductive Databases

Database Reformulation is the process of rewriting the data and rules in deductive databases in a functionally equivalent manner, ideally in ways that decrease query processing time while keeping storage costs within acceptable bounds. Early research in this area focussed on materializing existing views, i.e. caching those views as data. Subsequent research investigated the problem of inventing new views to afford different opportunities for materialization. The Bounding Theorem, introduced in this latter effort, is significant in that it gives a finite bound on the number of useful reformulations for conjunctive queries. Unfortunately, the number of possibilities allowed by the Bounding Theorem is doubly exponential in the size of the query (not the database instance). In this paper, we show that we can reduce that double exponential to a single exponential. We first present an improved version of the Bounding Theorem, called the Subgoal Theorem. We then present an additional result, called the Projection Theorem. Finally, we present a reformulation algorithm that runs in exponential time; and, using the Subgoal Theorem and the Projection Theorem, we show that the algorithm is correct for all conjunctive queries, i.e. it produces reformulations that are as good as or better than any other reformulation (in terms of worst-case query evaluation performance with at most linear growth in storage space).