Query folding refers to the activity of determining if and how a query can be answered using a given set of resources, which might be materialized views, cached results of previous queries, or queries answerable by another database. We investigate query folding in the context where queries and resources are conjunctive queries. We develop an exponential-time algorithm that finds all foldings, and a polynomial-time algorithm for the subclass of acyclic queries. Our results can be applied to query optimization in centralized databases, to query processing in distributed databases, and to query answering in federated databases. 1 Introduction Query folding refers to the activity of determining if and how a query can be answered using a given set of resources. These resources might be materialized views, cached results of previous queries, or even queries answerable by another database. Query folding is important because the base relations referred to in a query might be stored remotely a...

Presented is a computation method-the chase-for testing implication of data dependencies by a set of data dependencies. The chase operates on tableaux similar to those of Aho, Sagiv, and Ullman. The chase includes previous tableau computation methods as special cases. By interpreting tableaux alternately as mappings or as templates for relations, it is possible to test implication of join dependencies (including multivalued dependencies) and functional dependencies by a set of depen-dencies.

We consider the problems of conjunctive query containment and minimization, which are known to be NP-complete, and show that these problems can be solved in polynomial time for the class of acyclic queries. We then generalize the notion of acyclicity and define a parameter called query width that captures the "degree of cyclicity" of a query: in particular, a query is acyclic if and only if its query width is 1. We give algorithms for containment and minimization that run in time polynomial in n k , where n is the input size and k is the query width. These algorithms naturally generalize those for acyclic queries, and are of practical significance because many queries have small query width compared to their sizes. We show that good bounds on the query width of Q can be obtained using the treewidth of the incidence graph of Q. We then consider the problem of finding an equivalent query to a given conjunctive query Q that has the least number of subgoals. We show that a polynomial tim...

We consider the problem of answering queries from databases that may be incomplete. A database is incomplete if some tuples may be missing from some relations, and only a part of each relation is known to be complete. This problem arises in several contexts. For example, systems that provide access to multiple heterogeneous information sources often encounter incomplete sources. The question we address is to determine whether the answer to a specific given query is complete even when the database is incomplete. We present a novel sound and complete algorithm for the answer-completeness problem by relating it to the problem of independence of queries from updates. We also show an important case of the independence problem (and therefore of the answer-completeness problem) that can be decided in polynomial time, whereas the best known algorithm for this case is exponential. This case involves updates that are described using a conjunction of comparison predicates. We also describe an alg...

... In this paper, we describe the way the expressive power of the Carin language is exploited in the Picsel information integration system, while maintaining the decidability of query answering. We illustrate it on examples coming from the tourism domain, which is the first real case that we have to consider in Picsel, in collaboration with the travel agency Degriftour.

The management of semistructured data has recently received significant attention because of the need of several applications to model and query large volumes of irregular data. This paper considers the problem of query containment for a query language over semistructured data, StruQL0 , that contains the essential feature common to all such languages, namely the ability to specify regular path expressions over the data. We show here that containment of StruQL0 queries is decidable. First, we give a semantic criterion for StruQL0 query containment: we show that it suffices to check containment on only finitely many canonical databases. Second, we give a syntactic criteria for query containment, based on a notion of query mappings, which extends containment mappings for conjunctive queries. Third, we consider a certain fragment of StruQL0 , obtained by imposing restrictions on the regular path expressions, and show that query containment for this fragment of StruQL0 is NP complete. 1 ...

The problem of query containment is fundamental to many aspects of database systems,including query optimization,determining independence of queries from updates,and rewriting queries using views. In the data-integration framework,however,the standard notion of query containment does not suffice. We define relative containment,which formalizes the notion of query containment relative to the sources available to the data-integration system. First,we provide optimal bounds for relative containment for several important classes of datalog queries,including the common case of conjunctive queries. Next,we provide bounds for the case when sources enforce access restrictions in the form of binding pattern constraints. Surprisingly,we show that relative containment for conjunctive queries is still decidable in this case,even though it is known that finding all answers to such queries may require a recursive datalog program over the sources. Finally,we provide tight bounds for variants of relative containment when the queries and source descriptions may contain comparison predicates.

We address the problem of query containment and query equivalence for complex objects. We show that for a certain conjunctive query language for complex objects, query containment and weak query equivalence are decidable. Our results have two consequences. First, when the answers of the two queries are guaranteed not to contain empty sets, then weak equivalence coincides with equivalence, and our result answers partially an open problem about the equivalence of nest; unnest queries for complex objects [GPG90]. Second, we derive an NP-complete algorithm for checking the equivalence of certain conjunctive queries with grouping and aggregates. Our results rely on a translation of the containment and equivalence conditions for complex objects into novel conditions on conjunctive queries, which we call simulation and strong simulation. These conditions are more complex than containment of conjunctive queries, because they involve arbitrary numbers of quantifier alternations. We prove that c...

Answering queries posed over knowledge bases is a central problem in knowledge representation and database theory. In databases, query containment is one of the important query optimization and schema integration techniques [1, 12,16]; in knowledge representation, it has been used for object classification, schema integration, service discovery, and more, in particular in the area of description logics [6, 14]. Results on practical instances of the general problem were studied in [12], followed by [5, 7, 2, 4, 13]. In particular, [5] and [7] deal respectively with query containment and efficient query answering under expressive description logic constraints, that can express several construct used in conceptual data modeling; [2] and [4] address query containment under constraints derived respectively from entity-relationship and object-oriented formalisms. The complexity of reasoning tasks on complex constraints based on answer set programs has been investgated in [19]. The problem of query containment is strictly related to that of answering queries over knowledge bases; indeed, the two are mutually reducible; we focus on the former, and our results immediately extend to the

There has been growing interest in semantic query caches to aid in query evaluation. Semantic caches are simply the results of previously asked queries, or selected relational information chosen by an evaluation strategy, that have been cached locally. For complex environments such as distributed, heterogeneous databases and data warehousing, the use of semantic caches promises to help optimize query evaluation, increase turnaround for users, and reduce network load and other resource usage. We present a general logical framework for semantic caches. We consider the use of all relational operations across the caches for answering queries, and we consider the various ways to answer, and to partially answer, a query by cache. We address when answers are in cache, when answers in cache can be recovered, and the notions of semantic overlaps, semantic independence, and semantic query remainder. While there has been much work relevant to the use of semantic caches, no one has addressed in conjunction the issues pertinent to the effective use of semantic caches to evaluate queries. In some cases, this is due to overly simplified assumptions, and in other cases to the lack of a formal framework. We attempt to establish some of that framework here. Within that framework, we illustrate the issues involved in using semantic caches for query evaluation. We show various applications for semantic caches, and relate the work to relevant areas. 1