Conjunctive Queries and Mappings With Unequalities

We study conjunctive queries with unequalities (x ≠ y) and we identify cases when query containment can still be characterized by the existence of homomorphisms. We also identify a class of GLAV-like database schema mappings with unequalities, for which the chase theorem holds, and thus data exchange has the same complexity as for GLAV mappings. Finally, we define a notion of consistency and provide an algorithm to check whether a set of mappings is consistent

Consistency of injective tree patterns

International audienceTesting if an incomplete description of an XML document is consistent, that is, if it describes a real document conforming to the imposed schema, amounts to deciding if a given tree pattern can be matched injectively into a tree accepted by a fixed automaton. This problem can be solved in polynomial time for patterns that use the child relation and the sibling order, but do not use the descendant relation. For general patterns the problem is in NP, but no lower bound has been known so far. We show that the problem is NP-complete already for patterns using only child and descendant relations. The source of hardness turns out to be the interplay between these relations: for patterns using only descendant we give a polynomial algorithm. We also show that the algorithm can be adapted to patterns using descendant and following-sibling, but combining descendant and next-sibling leads to intractability

Approximation in Databases

One source of partial information in databases is the need to combine information from several databases. Even if each database is complete for some world , the combined databases will not be, and answers to queries against such combined databases can only be approximated. In this paper we describe various situations in which a precise answer cannot be obtained for a query asked against multiple databases. Based on an analysis of these situations, we propose a classification of constructs that can be used to model approximations. One of the main goals is to show that most of these models of approximations possess universality properties. The main motivation for doing this is applying the data-oriented approach, which turns universality properties into syntax, to obtain languages for approximations. We show that the languages arising from the universality properties have a number of limitations. In an attempt to overcome those limitations, we explain how all the languages can be embedded into a language for conjunctive and disjunctive sets from [21], and demonstrate its usefulness in querying independent databases

Data Exchange: Query Answering for Incomplete Data Sources

Data exchange is the problem of transforming data struc-tured under a schema, called the source schema, into data structured under another schema, called the target schema. Existing work on data exchange considers settings where the source instance does not contain incomplete information. In this paper we study semantics and address algorithmic issues for data exchange settings where the source instance may contain incomplete data. We investigate the query answer-ing problem in such data exchange settings. First we give two different meaningful semantics to certain answers: One via the certain answers in the corresponding complete data exchange problems and the other via the set of all solutions of the corresponding complete data exchange problems. We use the chase to compute a universal instance which is ma-terialized over the target schema and is used to compute the certain answers to unions of conjunctive queries. We prove that computing certain answers (under both semantics) for unions of conjunctive queries can be done in polynomial time when the schema mapping contains constraints that consist of a weakly acyclic set of tuple-generating dependencies and equality-generating dependencies. 1