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On the Decidability of Query Containment under Constraints
 IN PROC. OF THE 17TH ACM SIGACT SIGMOD SIGART SYMP. ON PRINCIPLES OF DATABASE SYSTEMS (PODS’98
, 1998
"... Query containment under constraints is the problem of checking whether for every database satisfying a given set of constraints, the result of one query is a subset of the result of another query. Recent research points out that this is a central problem in several database applications, and we addr ..."
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Cited by 242 (60 self)
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Query containment under constraints is the problem of checking whether for every database satisfying a given set of constraints, the result of one query is a subset of the result of another query. Recent research points out that this is a central problem in several database applications, and we address it within a setting where constraints are specified in the form of special inclusion dependencies over complex expressions, built by using intersection and difference of relations, special forms of quantification, regular expressions over binary relations, and cardinality constraints. These types of constraints capture a great variety of data models, including the relational, the entityrelational, and the objectoriented model. We study the problem of checking whether q is contained in q 0 with respect to the constraints specified in a schema S, where q and q 0 are nonrecursive Datalog programs whose atoms are complex expressions. We present the following results on query containme...
Query Folding
 In ICDE
, 1996
"... 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 resou ..."
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Cited by 138 (1 self)
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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 exponentialtime algorithm that finds all foldings, and a polynomialtime 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...
Conjunctive Query Containment Revisited
, 1998
"... We consider the problems of conjunctive query containment and minimization, which are known to be NPcomplete, 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 ca ..."
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Cited by 98 (0 self)
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We consider the problems of conjunctive query containment and minimization, which are known to be NPcomplete, 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...
Obtaining Complete Answers from Incomplete Databases
 In Proc. of the 22nd Int. Conf. on Very Large Data Bases (VLDB'96
, 1996
"... 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 ..."
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Cited by 84 (7 self)
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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 answercompleteness 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 answercompleteness 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...
Reformulation of XML Queries and Constraints
 In ICDT
, 2003
"... Abstract. We state and solve the query reformulation problem for XML publishing in a general setting that allows mixed (XML and relational) storage for the proprietary data and exploits redundancies (materialized views, indexes and caches) to enhance performance. The correspondence between published ..."
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Cited by 82 (14 self)
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Abstract. We state and solve the query reformulation problem for XML publishing in a general setting that allows mixed (XML and relational) storage for the proprietary data and exploits redundancies (materialized views, indexes and caches) to enhance performance. The correspondence between published and proprietary schemas is specified by views in both directions, and the same algorithm performs rewritingwithviews, compositionwithviews, or the combined effect of both, unifying the GlobalAsView and LocalAsView approaches to data integration. We prove a completeness theorem which guarantees that under certain conditions, our algorithm will find a minimal reformulation if one exists. Moreover, we identify conditions when this algorithm achieves optimal complexity bounds. We solve the reformulation problem for constraints by exploiting a reduction to the problem of query reformulation. 1
Rewriting Aggregate Queries Using Views
, 1999
"... We investigate the problem of rewriting queries with aggregate operators using views that mayormay not contain aggregate operators. A rewriting of a query is a second query that uses view predicates such that evaluating first the views and then the rewriting yields the same result as evaluating the ..."
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Cited by 71 (8 self)
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We investigate the problem of rewriting queries with aggregate operators using views that mayormay not contain aggregate operators. A rewriting of a query is a second query that uses view predicates such that evaluating first the views and then the rewriting yields the same result as evaluating the original query. In this sense, the original query and the rewriting are equivalent modulo the view definitions. The queries and views we consider correspond to unnested SQL queries, possibly with union, that employ the operators min, max, count, and sum. Our approach is based on syntactic characterizations of the equivalence of aggregate queries. One contribution of this paper are characterizations of the equivalence of disjunctive aggregate queries, which generalize our previous results for the conjunctive case. For each operator α, we introduce several types of queries using views as candidates for rewritings. We unfold such a candidate by replacing each occurrence of a view predicate with ...
Subsumption between Queries to ObjectOriented Databases
, 1994
"... Most work on query optimization in relational and objectoriented databases has concentrated on tuning algebraic expressions and the physical access to the database contents. The attention to semantic query optimization, however, has been restricted due to its inherent complexity. We take a second l ..."
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Cited by 66 (8 self)
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Most work on query optimization in relational and objectoriented databases has concentrated on tuning algebraic expressions and the physical access to the database contents. The attention to semantic query optimization, however, has been restricted due to its inherent complexity. We take a second look at the problem for queries in objectoriented databases and find that reasoning techniques for concept languages developed in Artificial Intelligence apply for the following reasons: concept languages have been tailored for efficiency and their semantics is compatible with class and query definitions in objectoriented databases. We propose a query optimizer which decides subset relationships between a query and a view (a simpler query whose answer is stored) in polynomial time. This work was supported in part by the Commission of the European Communities under ESPRIT Basic Research Action 6810 (Compulog 2), by the German Ministry of Research and Technology under grant ITW 9201 (TACOS...
Physical Data Independence, Constraints, and Optimization with Universal Plans
, 1999
"... We present an optimization method and algorithm designed for three objectives: physical data independence, semantic optimization, and generalized tableau minimization. The method relies on generalized forms of chase and "backchase" with constraints (dependencies). By using dictionaries (finite funct ..."
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Cited by 42 (11 self)
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We present an optimization method and algorithm designed for three objectives: physical data independence, semantic optimization, and generalized tableau minimization. The method relies on generalized forms of chase and "backchase" with constraints (dependencies). By using dictionaries (finite functions) in physical schemas we can capture with constraints useful access structures such as indexes, materialized views, source capabilities, access support relations, gmaps, etc. The search space for query plans is de ned and enumerated in a novel manner: the chase phase rewrites the original query into a "universal" plan that integrates all the access structures and alternative pathways that are allowed by applicable constraints. Then, the backchase phase produces optimal plans by eliminating various combinations of redundancies, again according to constraints. This method is applicable (sound) to a large class of queries, physical access structures, and semantic constraints. We prove that it is in fact complete for "pathconjunctive" queries and views with complex objects, classes and dictionaries, going beyond previous theoretical work on processing queries using materialized views.
Solving Satisfiability and Implication Problems in Database Systems
 ACM Transactions on Database Systems
, 1996
"... Satisfiability, implication, and equivalence problems involving conjunctive inequalities are important and widely encountered database problems that need to be efficiently and effectively processed. In this article we consider two popular types of arithmetic inequalities, (X op Y) and (X op C), wher ..."
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Cited by 39 (0 self)
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Satisfiability, implication, and equivalence problems involving conjunctive inequalities are important and widely encountered database problems that need to be efficiently and effectively processed. In this article we consider two popular types of arithmetic inequalities, (X op Y) and (X op C), where X and Y are attributes, C is a constant of the domain or X, and op � {�, �, �, �, �, �}. These inequalities are most frequently used in a database system, inasmuch as the former type of inequality represents a �—join, and the latter is a selection. We study the satisfiability and implication problems under the integer domain and the real domain, as well as under two different operator sets ({�, �, �, �, �} and {�,�,�,�,�,�}). Our results show that solutions under different domains and/or different operator sets are quite different. Out of these eight cases, excluding two cases that had been shown to be NPhard, we either report the first necessary and sufficient conditions for these problems as well as their efficient algorithms with complexity analysis (for four cases), or provide an improved algorithm (for two cases). These iff conditions and algorithms are essential to database designers, practitioners, and researchers. These algorithms have been implemented and an experimental study comparing the proposed algorithms and those previously known is conducted. Our experiments show that the proposed algorithms are more efficient than previously known algorithms even for small input. Categories and Subject Descriptors: H.2.4 [Database Management]: Systems—query processing;
Conjunctive query containment and answering under description logics constraints
 ACM TRANS. ON COMPUTATIONAL
, 2008
"... Query containment and query answering are two important computational tasks in databases. While query answering amounts to compute the result of a query over a database, query containment is the problem of checking whether for every database, the result of one query is a subset of the result of anot ..."
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Cited by 32 (14 self)
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Query containment and query answering are two important computational tasks in databases. While query answering amounts to compute the result of a query over a database, query containment is the problem of checking whether for every database, the result of one query is a subset of the result of another query. In this paper, we deal with unions of conjunctive queries, and we address query containment and query answering under Description Logic constraints. Every such constraint is essentially an inclusion dependency between concepts and relations, and their expressive power is due to the possibility of using complex expressions in the specification of the dependencies, e.g., intersection and difference of relations, special forms of quantification, regular expressions over binary relations. These types of constraints capture a great variety of data models, including the relational, the entityrelationship, and the objectoriented model, all extended with various forms of constraints. They also capture the basic features of the ontology languages used in the context of the Semantic Web. We present the following results on both query containment and query answering. We provide a method for query containment under Description Logic constraints, thus showing that the problem