Scalable containment for unions of conjunctive queries under constraints

We consider the problem of query containment under ontological constraints, such as those of RDFS. Query containment, i.e., deciding whether the answers of a given query are always contained in the answers of another query, is an important problem to areas such as database theory and knowledge representation, with applications to data integration, query optimization and minimization. We consider unions of conjunctive queries, which constitute the core of structured query languages, such as SPARQL and SQL. We also consider ontological constraints or axioms, expressed in the language of Tuple-Generating Dependencies. TGDs capture RDF/S and fragments of Description Logics. We consider classes of TGDs for which the chase is known to terminate. Query containment under chase-terminating axioms can be decided by first running the chase on one of the two queries and then rely on classic relational containment. When considering unions of conjunctive queries, classic algorithms for both the chase and containment phases suffer from a large degree of redundancy. We leverage a graph-based modeling of rules, that represents multiple queries in a compact form, by exploiting shared patterns amongst them. As a result we couple the phases of both for chase and regular containment and end up with a faster and more scalable algorithm. Our experiments show a speedup of close to two orders of magnitude.