On conjunctive queries containing inequalities

Abstract

Conjunctive queries are generalized so that inequality comparisons can be made between elements of the query. Algorithms for containment and equivalence of such “inequality queries” are given, under the assumption that the data domains are dense and totally ordered. In general, containment does not imply the existence of homomorphisms (containment mappings), but the homomorphism property does exist for subclasses of inequality queries. A minimization algorithm is defined using the equivalence algorithm. It is first shown that the constants appearing in a query can be divided into “essential” and “nonessential” subgroups. The minimum query can be nondeterministically guessed using only the essential constants of the original query.