The power of tree projections
Gianluigi Greco, Francesco Scarcello · 2010
Enforcing local consistency is a well-known technique to simplify the evaluation of conjunctive queries. It consists of repeatedly taking the semijion between every pair of (relations associated with) query atoms, until the procedure stabilizes. If some relation becomes empty, then the query has an empty answer. Otherwise, we cannot say anything in general, unless we have some information on the structure of the given query. In fact, a fundamental result in database theory states that the class of queries for which---on every database---local consistency entails global consistency is precisely the class of acyclic queries. In the last few years, several efforts have been made to define structural decomposition methods isolating larger classes of nearly-acyclic queries, yet retaining the same nice properties as acyclic ones. In particular, it is known that queries having bounded (generalized) hypertree-width can be evaluated in polynomial time, and that this structural property is also sufficient to guarantee that local consistency solves the problem, as for acyclic queries. However, the precise power of such an approach was an open problem: Is it the case that bounded generalized hypertree-width is also a necessary condition to guarantee that local consistency entails global consistency?