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108
Composition of Mappings Given by Embedded Dependencies
 In PODS
, 2005
"... Composition of mappings between schemas is essential to support schema evolution, data exchange, data integration, and other data management tasks. In many applications, mappings are given by embedded dependencies. In this paper, we study the issues involved in composing such mappings. Our algorithm ..."
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Cited by 52 (11 self)
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Composition of mappings between schemas is essential to support schema evolution, data exchange, data integration, and other data management tasks. In many applications, mappings are given by embedded dependencies. In this paper, we study the issues involved in composing such mappings. Our algorithms and results extend those of Fagin et al. [8] who studied composition of mappings given by several kinds of constraints. In particular, they proved that full sourcetotarget tuplegenerating dependencies (tgds) are closed under composition, but embedded sourcetotarget tgds are not. They introduced a class of secondorder constraints, SO tgds, that is closed under composition and has desirable properties for data exchange. We study constraints that need not be sourcetotarget and we concentrate on obtaining (firstorder) embedded dependencies. As part of this study, we also consider full dependencies and secondorder constraints that arise from Skolemizing embedded dependencies. For each of the three classes of mappings that we study, we provide (a) an algorithm that attempts to compute the composition and (b) sufficient conditions on the input mappings that guarantee that the algorithm will succeed. In addition, we give several negative results. In particular, we show that full dependencies are not closed under composition, and that secondorder dependencies that are not limited to be sourcetotarget are not closed under restricted composition. Furthermore, we show that determining whether the composition can be given by these kinds of dependencies is undecidable. 1.
Rewriting queries using views with access patterns under integrity constraints
, 2007
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Probabilistic data exchange
 In Proc. ICDT
, 2010
"... The work reported here lays the foundations of data exchange in the presence of probabilistic data. This requires rethinking the very basic concepts of traditional data exchange, such as solution, universal solution, and the certain answers of target queries. We develop a framework for data exchange ..."
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Cited by 43 (7 self)
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The work reported here lays the foundations of data exchange in the presence of probabilistic data. This requires rethinking the very basic concepts of traditional data exchange, such as solution, universal solution, and the certain answers of target queries. We develop a framework for data exchange over probabilistic databases, and make a case for its coherence and robustness. This framework applies to arbitrary schema mappings, and finite or countably infinite probability spaces on the source and target instances. After establishing this framework and formulating the key concepts, we study the application of the framework to a concrete and practical setting where probabilistic databases are compactly encoded by means of annotations formulated over random Boolean variables. In this setting, we study the problems of testing for the existence of solutions and universal solutions, materializing such solutions, and evaluating target queries (for unions of conjunctive queries) in both the exact sense and the approximate sense. For each of the problems, we carry out a complexity analysis based on properties of the annotation, in various classes of dependencies. Finally, we show that the framework and results easily and completely generalize to allow not only the data, but also the schema mapping itself to be probabilistic.
On the minimization of XPath queries
 In VLDB
, 2003
"... XML queries are usually expressed by means of XPath expressions identifying portions of the selected documents. An XPath expression defines a way of navigating an XML tree and returns the set of nodes which are reachable from one or more starting nodes through the paths specified by the expression. ..."
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Cited by 40 (0 self)
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XML queries are usually expressed by means of XPath expressions identifying portions of the selected documents. An XPath expression defines a way of navigating an XML tree and returns the set of nodes which are reachable from one or more starting nodes through the paths specified by the expression. The problem of efficiently answering XPath queries is very interesting and has recently received increasing attention by the research community. In particular, an increasing effort has been devoted to define effective optimization techniques for XPath queries. One of the main issues related to the optimization of XPath queries is their minimization. The minimization of XPath queries has been studied for limited fragments of XPath, containing only the descendent, the child and the branch operators. In this work, we address the problem of minimizing XPath queries for a more general fragment, containing also the wildcard operator. We characterize the complexity of the minimization of XPath queries, stating that it is NPhard, and propose an algorithm for computing minimum XPath queries. Moreover, we identify an interesting tractable case and propose an ad hoc algorithm handling the minimization of this kind of queries in polynomial time.
Query reformulation with constraints
 SIGMOD Record
"... Let Σ1, Σ2 be two schemas, which may overlap, C be a set of constraints on the joint schema Σ1 ∪ Σ2, and q1 be a Σ1query. An (equivalent) reformulation of q1 in the presence of C is a Σ2query, q2, such that q2 gives the same answers as q1 on ..."
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Cited by 38 (4 self)
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Let Σ1, Σ2 be two schemas, which may overlap, C be a set of constraints on the joint schema Σ1 ∪ Σ2, and q1 be a Σ1query. An (equivalent) reformulation of q1 in the presence of C is a Σ2query, q2, such that q2 gives the same answers as q1 on
Towards a Theory of SchemaMapping Optimization
, 2008
"... A schema mapping is a highlevel specification that describes the relationship between two database schemas. As schema mappings constitute the essential building blocks of data exchange and data integration, an extensive investigation of the foundations of schema mappings has been carried out in rec ..."
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Cited by 38 (7 self)
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A schema mapping is a highlevel specification that describes the relationship between two database schemas. As schema mappings constitute the essential building blocks of data exchange and data integration, an extensive investigation of the foundations of schema mappings has been carried out in recent years. Even though several different aspects of schema mappings have been explored in considerable depth, the study of schemamapping optimization remains largely uncharted territory to date. In this paper, we lay the foundation for the development of a theory of schemamapping optimization. Since schema mappings are constructs that live at the logical level of information integration systems, the first step is to introduce concepts and to develop techniques for transforming schema mappings to “equivalent ” ones that are more manageable from the standpoint of data exchange or of some other data interoperability task. In turn, this has to start by introducing and studying suitable notions of “equivalence ” between schema mappings. To this effect, we introduce the concept of dataexchange equivalence and the concept of conjunctivequery equivalence. These two concepts of equivalence are natural relaxations of the classical notion of logical equivalence; the first captures indistinguishability for dataexchange purposes, while the second captures indistinguishability for conjunctivequeryanswering purposes. Moreover, they coincide with logical equivalence on schema mappings specified by sourcetotarget tuplegenerating dependencies (st tgds), but differ on richer classes of dependencies, such as secondorder tuplegenerating dependencies (SO tgds) and sets of st tgds and target tuplegenerating dependencies (target tgds). After exploring the basic properties of these three notions of equivalence between schema mappings, we focus on the following question: under what conditions is a schema mapping conjunctivequery equivalent to a schema mapping specified by a finite set of st tgds? We answer this question by obtaining complete characteriza
The Recovery of a Schema Mapping: Bringing Exchanged Data Back
 In Proceedings of the 28th ACM Symposium on Principles of Database Systems (PODS
, 2008
"... A schema mapping is a specification that describes how data from a source schema is to be mapped to a target schema. Once the data has been transferred from the source to the target, a natural question is whether one can undo the process and recover the initial data, or at least part of it. In fact, ..."
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Cited by 38 (13 self)
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A schema mapping is a specification that describes how data from a source schema is to be mapped to a target schema. Once the data has been transferred from the source to the target, a natural question is whether one can undo the process and recover the initial data, or at least part of it. In fact, it would be desirable to find a reverse schema mapping from target to source that specifies how to bring the exchanged data back. In this paper, we introduce the notion of a recovery of a schema mapping: it is a reverse mapping M ′ for a mapping M that recovers sound data with respect to M. We further introduce an order relation on recoveries. This allows us to choose mappings that recover the maximum amount of sound information. We call such mappings maximum recoveries. We study maximum recoveries in detail, providing a necessary and sufficient condition for their existence. In particular, we prove that maximum recoveries exist for the class of mappings specified by FOTOCQ sourcetotarget dependencies. This class subsumes the class of sourcetotarget tuplegenerating dependencies used in previous work on data exchange. For the class of mappings specified by FOTOCQ dependencies, we provide an exponentialtime algorithm for computing maximum recoveries, and a simplified version for full dependencies that works in quadratic time. We also characterize the language needed to express maximum recoveries, and we include a detailed comparison with the notion of inverse (and quasiinverse) mapping previously proposed in the data exchange literature. In particular, we show that maximum recoveries strictly generalize inverses. We finally study the complexity of some decision problems related to the notions of recovery and maximum recovery.
Logical foundations of relational data exchange
 SIGMOD Record
"... Data exchange has been defined as the problem of taking data structured under a source schema and materializing an instance of a target schema that reflects as accurately as possible the source data [19]. In the last years, the need ..."
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Cited by 38 (3 self)
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Data exchange has been defined as the problem of taking data structured under a source schema and materializing an instance of a target schema that reflects as accurately as possible the source data [19]. In the last years, the need
Repair Checking in Inconsistent Databases: Algorithms and Complexity
 Proc. of the International Conference on Database Theory (ICDT
"... Managing inconsistency in databases has long been recognized as an important problem. One of the most promising approaches to coping with inconsistency in databases is the framework of database repairs, which has been the topic of an extensive investigation over the past several years. Intuitively, ..."
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Cited by 37 (3 self)
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Managing inconsistency in databases has long been recognized as an important problem. One of the most promising approaches to coping with inconsistency in databases is the framework of database repairs, which has been the topic of an extensive investigation over the past several years. Intuitively, a repair of an inconsistent database is a consistent database that differs from the given inconsistent database in a minimal way. So far, most of the work in this area has addressed the problem of obtaining the consistent answers to a query posed on an inconsistent database. Repair checking is the following decision problem: given two databases r and r ′ , is r ′ a repair of r? Although repair checking is a fundamental algorithmic problem about inconsistent databases, it has not received as much attention as consistent query answering. In this paper, we give a polynomialtime algorithm for subsetrepair checking under integrity constraints that are the union of a weakly acyclic set of localasview (LAV) tuplegenerating dependencies and a set of equalitygenerating dependencies. This result significantly generalizes earlier work for subsetrepair checking when the integrity constraints are the union of an acyclic set of inclusion dependencies and a set of functional dependencies. We also give a polynomialtime algorithm for symmetricdifference repair checking, when the integrity constraints form a weakly acyclic set of LAV tgds. After this, we establish a number of complexitytheoretic results that delineate the boundary between tractability and intractability for the repairchecking problem. Specifically, we show that the aforementioned tractability
A Better Uncle For OWL  Nominal Schemas for Integrating Rules and Ontologies
, 2011
"... We propose a descriptionlogic style extension of OWL 2 with nominal schemas which can be used like “variable nominal classes”within axioms. This feature allows ontology languages to express arbitrary DLsafe rules (as expressible in SWRL or RIF) in their native syntax. We show that adding nominal s ..."
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Cited by 37 (17 self)
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We propose a descriptionlogic style extension of OWL 2 with nominal schemas which can be used like “variable nominal classes”within axioms. This feature allows ontology languages to express arbitrary DLsafe rules (as expressible in SWRL or RIF) in their native syntax. We show that adding nominal schemas to OWL 2 does not increase the worstcase reasoning complexity, and we identify a novel tractable language SROELV 3(⊓, ×) that is versatile enough to capture the lightweight languages OWL EL and OWL RL.