Optimizing conjunctive queries when attribute domains are not disjoint

We present polynomial time algorithms for minimizing and testing equivalence of what we call "fan-out free" queries. The fan-out free queries form a more general and more powerful subclass of the conjunctive queries than those previously studied, as they can be used to express questions about transitive properties of databases, questions that are impossible to express if one operates under the "disjoint domain assumption" implicit in previous work. Our algorithms are graph-theoretic in nature, and the equivalence algorithm can be viewed as solving a special case of the graph isomorphism problem (by reducing it to a series of labelled forest isomorphism questions).