Efficient approximations of conjunctive queries

When finding exact answers to a query over a large database is infeasible, it is natural to approximate the query by a more efficient one that comes from a class with good bounds on the complexity of query evaluation. In this paper we study such approximations for conjunctive queries. These queries are of special importance in databases, and we have a very good understanding of the classes that admit fast query evaluation, such as acyclic, or bounded (hyper)treewidth queries. We define approximations of a given query Q as queries from one of those classes that disagree with Q as little as possible. We mostly concentrate on approximations that are guaranteed to return correct answers. We prove that for the above classes of tractable conjunctive queries, approximations always exist, and are at most polynomial in the size of the original query. This follows from general results we establish that relate closure properties of classes of conjunctive queries to the existence of approximations. We also show that in many cases, the size of approximations is bounded by the size of the query they approximate. We establish a number of results showing how combinatorial properties of queries affect properties of their approximations, study bounds on the number of approximations, as well as the complexity of finding and identifying approximations. We also look at approximations that return all correct answers and study their properties

On Low Treewidth Approximations of Conjunctive Queries

We recently initiated the study of approximations of conjunctive queries within classes that admit tractable query evaluation (with respect to combined complexity). Those include classes of acyclic, bounded treewidth, or bounded hypertreewidth queries. Such approximations are always guaranteed to exist. However, while for acyclic and bounded hypertreewidth queries we have shown a number of examples of interesting approximations, for queries of bounded treewidth the study had been restricted to queries over graphs, where such approximations usually trivialize. In this note we show that for relations of arity greater than two, the notion of low treewidth approximations is a rich one, as many queries possess them. In fact we look at approximations of queries of maximum possible treewidth by queries of minimum possible treewidth (i.e., one), and show that even in this case the structure of approximations remain rather rich as long as input relations are not binary

Oblivious Bounds on the Probability of Boolean Functions

This paper develops upper and lower bounds for the probability of Boolean functions by treating multiple occurrences of variables as independent and assigning them new individual probabilities. We call this approach dissociation and give an exact characterization of optimal oblivious bounds, i.e. when the new probabilities are chosen independent of the probabilities of all other variables. Our motivation comes from the weighted model counting problem (or, equivalently, the problem of computing the probability of a Boolean function), which is #P-hard in general. By performing several dissociations, one can transform a Boolean formula whose probability is difficult to compute, into one whose probability is easy to compute, and which is guaranteed to provide an upper or lower bound on the probability of the original formula by choosing appropriate probabilities for the dissociated variables. Our new bounds shed light on the connection between previous relaxation-based and model-based approximations and unify them as concrete choices in a larger design space. We also show how our theory allows a standard relational database management system (DBMS) to both upper and lower bound hard probabilistic queries in guaranteed polynomial time.Comment: 34 pages, 14 figures, supersedes: http://arxiv.org/abs/1105.281

Module extraction via query inseparability in OWL 2 QL

We show that deciding conjunctive query inseparability for OWL 2 QL ontologies is PSpace-hard and in ExpTime. We give polynomial-time (incomplete) algorithms and demonstrate by experiments that they can be used for practical module extraction

Trio-One: Layering Uncertainty and Lineage on a Conventional DBMS

Trio is a new kind of database system that supports data, uncertainty, and lineage in a fully integrated manner. The first Trio prototype, dubbed Trio-One, is built on top of a conventional DBMS using data and query translation techniques together with a small number of stored procedures. This paper describes Trio-One's translation scheme and system architecture, showing how it efficiently and easily supports the Trio data model and query language