Tableaux-based optimization of schema mappings for data integration

Approximate top-K answering under uncertain schema mappings

Schema mappings are high-level specifications that describe the relationship between two database schemas. They are considered to be the essential building blocks in data exchange and data integration, and have been the focus of extensive research investigations. Since in real-life applications schema mappings can be quite complex, it is important to develop methods and tools for illustrating, explaining, and deriving schema mappings. A promising approach to this effect is to use "good" data examples that illustrate the schema mapping at hand.

Peer data management systems (PDMS) are the natural extension of integrated information systems. Conventionally, a single integrating system manages an integrated schema, distributes queries to appropriate sources, and integrates incoming data to a common result. In contrast, a PDMS consists of a set of peers, each of which can play the role of an integrating component. A peer knows about its neighboring peers by mappings, which help to translate queries and transform data. Queries submitted to one peer are answered by data residing at that peer and by data that is reached along paths of mappings through the network of peers. The only restriction for PDMS to cover unbounded data is the need to formulate at least one mapping from some known peer to a new data source. We propose a Semantic Web based method that overcomes this restriction, albeit at a price. As sources are dynamically and automatically included in a PDMS, three factors diminish quality: The new source itself might store data of poor quality, the mapping to the PDMS might be incorrect, and the mapping to the PDMS might be incomplete. To compensate, we propose a quality model to measure this effect, a cost model to restrict query planning to the best paths through the PDMS, and techniques to answer queries in such Webscale PDMS efficiently. 1 An Ever-growing PDMS The step from centralized database systems (DBMS) to distributed and then to federated database systems (FDBMS) removed the assumption that data must be located at the same site as the query. A federated database provides a global schema that represents the data it can access locally and remotely. The global schema is related to the local schemata via schema mappings, which specify how the schema of a local database maps to the global schema. The federated database accepts a query against its global schema and distributes it according to the schema mappings to the different sites where the data resides. Those sites execute the partial queries and send results back to the requesting peer. Again, the schema mappings specify how data is to be translated to conform to the global schema. The results are further processed and combined to be finally fused into a single response to the user. A natural extension to this paradigm is to remove the assumption that queries are only asked against a single integrating site. Peer data management systems (PDMS) are built of multiple peers, each of which provides a schema and accepts queries against the schema. Again, the peers are connected by mappings among their schemata. However, instead of forming a tree with a single root, each peer can be connected to any number of other peers. Queries against a schema of one peer can be answered using the data of the entire PDMS, as long as appropriate mappings have been formed (see Fig. 1). In general, a query

Data exchange is the problem of transforming data structured under a source schema into data structured under a target schema in such a way that all constraints of a schema mapping are satisfied. At the heart of data exchange, lies a basic decision problem, called the existence-of-solutions problem: given a source instance, is there a target instance that satisfies the constraints of the schema mapping at hand? Earlier work showed that for schema mappings specified by embedded implicational dependencies, this problem is solvable in polynomial time, assuming that (1) the schema mapping is kept fixed and (2) the constraints of the schema mapping satisfy a certain structural condition, called weak acyclicity.We investigate the effect of these assumptions on the complexity of the existence-of-solutions problem, and show that each one is indispensable in deriving polynomial-time algorithms for this problem. Specifically, using machinery from universal algebra, we show that if the weak acyclicity assumption is relaxed even in a minimal way, then the existence-of-solutions problem becomes undecidable. We also show that if, in addition to the source instance, the schema mapping is part of the input, then the existence-of-solutions problem becomes EXPTIME-complete. Thus, there is a provable exponential gap between the data complexity and the combined complexity of data exchange. Finally, we study restricted classes of schema mappings and develop a comprehensive picture for the combined complexity of the existence-of-solutions problem for these restrictions. In particular, depending on the restriction considered, the combined complexity of this problem turns out to be either EXPTIME-complete or coNP-complete.

Recently, two relaxed notions of equivalence of schema mappings have been introduced, which provide more potential of optimizing schema mappings than logical equivalence: data exchange (DE) equivalence and conjunctive query (CQ) equivalence. In this work, we systematically investigate these notions of equivalence for mappings consisting of s-t tgds and target egds and/or target tgds. We prove that both CQ- and DE-equivalence are undecidable and so are some important optimization tasks (like detecting if some dependency is redundant). However, we also identify an important difference between the two notions of equivalence: CQ-equivalence remains undecidable even if the schema mappings consist of s-t tgds and target dependencies in the form of key dependencies only. In contrast, DE-equivalence is decidable for schema mappings with s-t tgds and target dependencies in the form of functional and inclusion dependencies with terminating chase property.

This paper presents a schema mapping technique for XML-based geodata translation/transformation. XML is becoming the universal language for data exchange over the Internet. For geodata exchange, OGC defined the XML-based GML(Geographical Markup Language). Defining XML-based data format alone is not enough for data exchange. Associated techniques are equally important. The proposed schema mapping technique enables to a large extent automatic generation of geodata translator/convertor. Given a pair of source and target data schemas, a user specifies elements correspondence between them in a declarative way. The proposed schema mapping processor takes the schema mapping specification as input and generate geodata translator as output. Due to the automatic generation, semantic reconciliation between source and target schemas is very much facilitated.

This paper reports our first set of results on managing uncertainty in data integration. We posit that data-integration systems need to handle uncertainty at three levels, and do so in a principled fashion. First, the semantic mappings between the data sources and the mediated schema may be approximate because there may be too many of them to be created and maintained or because in some domains (e.g., bioinformatics) it is not clear what the mappings should be. Second, queries to the system may be posed with keywords rather than in a structured form. Third, the data from the sources may be extracted using information extraction techniques and so may yield imprecise data. As a first step to building such a system, we introduce the concept of probabilistic schema mappings and analyze their formal foundations. We show that there are two possible semantics for such mappings: by-table semantics assumes that there exists a correct mapping but we don't know what it is; by-tuple semantics assumes that the correct mapping may depend on the particular tuple in the source data. We present the query complexity and algorithms for answering queries in the presence of approximate schema mappings, and we describe an algorithm for efficiently computing the top-k answers to queries in such a setting.

A schema mapping is a high-level declarative specification of how data structured under one schema, called the source schema, is to be transformed into data structured under a possibly different schema, called the target schema. We demonstrate SPIDER, a prototype tool for debugging schema mappings, where the language for specifying schema mappings is based on a widely adopted formalism. We have built SPIDER on top of a data exchange system, Clio, from IBM Almaden Research Center. At the heart of SPIDER is a data-driven facility for understanding a schema mapping through the display of routes. A route essentially describes the relationship between source and target data with the schema mapping. In this demonstration, we showcase our route engine, where we can display one or all routes starting from either source or target data, as well as the intermediary data and schema elements involved. In addition, we demonstrate standard debugging features for schema mappings that we have also built, such as computing and exploring routes step-by-step, stopping or pausing the computation with breakpoints, performing guided computation of routes by taking human input into account, as well as tracking the state of the target instance during the process of computing routes.

Recently, two relaxed notions of equivalence of schema mappings have been introduced, which provide more potential of optimizing schema mappings than logical equivalence: data exchange (DE) equivalence and conjunctive query (CQ) equivalence. In this work, we systematically investigate these notions of equivalence for mappings consisting of s-t tgds and target egds and/or target tgds. We prove that both CQ- and DE-equivalence are undecidable and so are some important optimization tasks (like detecting if some dependency is redundant). However, we also identify an important difference between the two notions of equivalence: CQ-equivalence remains undecidable even if the schema mappings consist of s-t tgds and target dependencies in the form of key dependencies only. In contrast, DE-equivalence is decidable for schema mappings with s-t tgds and target dependencies in the form of functional and inclusion dependencies with terminating chase property.

The goal of data integration is to provide a uniform access to a set of heterogeneous data sources, freeing the user from the knowledge about where the data are, how they are stored, and how they can be accessed. One of the outcomes of the research work carried out on data integration in the last years is a clear conceptual architecture, comprising a global schema, the source schema, and the mapping between the source and the global schema. In this paper, we present a comprehensive approach to, and a complete system for, ontology-based data integration. In this system, the global schema is expressed in terms of a TBox of the tractable Description Logics ${\textit{DL-Lite}_{\mathcal A}}$, the sources are relations, and the mapping language allows for expressing GAV sound mappings between the sources and the global schema. The mapping language has specific mechanisms for addressing the so-called impedance mismatch problem, arising from the fact that, while the data sources store values, the instances of concepts in the ontology are objects. By virtue of the careful design of the various languages used in our system, answering unions of conjunctive queries can be done through a very efficient technique ( LogSpace with respect to data complexity) which reduces this task to standard SQL query evaluation. We also show that even very slight extensions of the expressive abilities of our system lead beyond this complexity bound.

The goal of data integration is to provide a uniform access to a set of heterogeneous data sources, freeing the user from the knowledge about where the data are, how they are stored, and how they can be accessed. One of the outcomes of the research work carried out on data integration in the last years is a clear conceptual architecture, comprising a global schema, the source schema, and the mapping between the source and the global schema. In this paper, we present a comprehensive approach to, and a complete system for, ontology-based data inte- gration. In this system, the global schema is expressed in terms of a TBox of the tractable Description Logics DL-LiteA, the sources are relations, and the map- ping language allows for expressing GAV sound mappings between the sources and the global schema. The mapping language has specific mechanisms for ad- dressing the so-called impedance mismatch problem, arising from the fact that, while the data sources store values, the instances of concepts in the ontology are objects. By virtue of the careful design of the various languages used in our sys- tem, answering unions of conjunctive queries can be done through a very efficient technique (LOGSPACE with respect to data complexity) which reduces this task to standard SQL query evaluation. We also show that even very slight extensions of the expressive abilities of our system lead beyond this complexity bound.

Data integration is the flexible and managed federation, analysis, and processing of data from different distributed sources. Data integration is becoming as important as data mining for exploiting the value of large and distributed data sets that are available today. Distributed processing infrastructures such as Grids can be used for data integration on geographically distributed sites. This paper presents a framework for integrating heterogeneous XML data sources distributed among the nodes of a Grid. We propose a query reformulation algorithm to combine and query XML documents through a decentralized point-to-point mediation process among the different data sources based on schema mappings. The above cited XML integration formalism is exposed as a Grid Service within the GDIS architecture. GDIS is a service-based architecture for providing data integration in Grids using a decentralized approach. The underlying model of such architecture is discussed and we show how it fits the XMAP formalism/algorithm.

Relational schema mappings have been extensively studied in connection with data integration and exchange problems, but mappings between XML schemas have not received the same amount of attention. Our goal is to develop a theory of expressive XML schema mappings. Such mappings should be able to use various forms of navigation in a document, and specify conditions on data values. We develop a language for XML schema mappings, and concentrate on three types of problems: static analysis of mappings, their complexity, and their composition. We look at static analysis problems related to various flavors of consistency: for example, whether it is possible to map some document of a source schema into a document of the target schema, or whether all documents of a source schema can be mapped. We classify the complexity of these problems. We then move to the complexity of mappings themselves, i.e., recognizing pairs of documents such that one can be mapped into the other, and provide a classification based on sets of features used in mappings. Finally we look at composition of XML schema mappings. We study its complexity and show that it is harder to achieve closure under composition for XML than for relational mappings. Nevertheless, we find a robust class of XML schema mappings that have good complexity properties and are closed under composition.

Schema mapping is becoming pervasive in all data transformation, exchange, and integration tasks. It brings to the surface the problem of differences and mismatches between heterogeneous formats and models, respectively, used in source and target databases to be mapped one to another. In this chapter, we start by describing the problem of schema mapping, its background, and technical implications. Then, we outline the early schema mapping systems, along with the new generation of schema mapping tools. Moving from the former to the latter entailed a dramatic change in the performance of mapping generation algorithms. Finally, we conclude the chapter by revisiting the query answering techniques allowed by the mappings, and by discussing useful applications and future and current developments of schema mapping tools.

With the popularity of the internet, more and more data are generated on internet. Because of the usability of Extensible Markup Language(XML for short), more data is organized by XML document format. Because of the flexibility of XML, data organized by XML have a variety of organizational formats which brings a lot of inconvenience to data management. In particular, when the large-scale data operations are performed on XML data, for example data integration, model change, and so on, there are many problems. One of the current implementations is to use Data Exchange to carry out the above operations. The works of predecessors mainly are to analyze the characteristics of Schema Mapping on XML, and institute Data Exchange rules. These rules only consider the data integrity, reliability, but don't consider the quality of the data after conversion. This paper proposes the concept of quality assurance mechanisms. Firstly we discuss that a new model with quality assurance, and provide a suitable method for this model. Then we propose the strategy of weak branch's convergence on the basis of Schema. In the end theoretical analysis and experimental results show that the method is correct and feasible.