Conjunctive Query Containment Revisited

We consider the problems of conjunctive query containment and minimization, which are known to be NP-complete, and show that these problems can be solved in polynomial time for the class of acyclic queries. We then generalize the notion of acyclicity and deene a parameter called query width that captures the \degree of cyclicity" of a query: in particular, a query is acyclic if and only if its query width is 1. We give algorithms for containment and minimization that run in time polynomial in n k , where n is the input size and k is the query width. These algorithms naturally generalize those for acyclic queries, and are of practical signi-cance because many queries have small query width compared to their sizes. We show that we can obtain good bounds on the query width of Q using the treewidth of the incidence graph of Q. Finally, we apply our containment algorithm to the practically important problem of nding equivalent rewritings of a query using a set of materialized views.