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.

A schema mapping is a high-level 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 schema-mapping optimization remains largely uncharted territory to date. In this paper, we lay the foundation for the development of a theory of schema-mapping 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 conjunctive-query equivalence. These two concepts of equivalence are natural relaxations of the classical notion of logical equivalence; the first captures indistinguishability for data-exchange purposes, while the second captures indistinguishability for conjunctive-query-answering purposes. Moreover, they coincide with logical equivalence on schema mappings specified by source-to-target tuple-generating dependencies (s-t tgds), but differ on richer classes of dependencies, such as second-order tuple-generating dependencies (SO tgds) and sets of s-t tgds and target tuple-generating 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 s-t tgds? We answer this question by obtaining complete characteriza-

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

Abstract. Much data is published on the Web in XML format satisfying schemas, and to make the Semantic Web a reality, such data needs to be interpreted with respect to ontologies. Interpretation is achieved through a semantic mapping between the XML schema and the ontology. We present work on the heuristic construction of complex such semantic mappings, when given an initial set of simple correspondences from XML schema attributes to datatype properties in the ontology. To accomplish this, we first offer a mapping formalism to capture the semantics of XML schemas. Second, we present our heuristic mapping construction algorithm. Finally, we show through an empirical study that considerable effort can be saved when constructing complex mappings by using our prototype tool. 1

Data exchange and virtual data integration have been the subject of several investigations in the recent literature. At the same time, the notion of peer data management has emerged as a powerful abstraction of many forms of flexible and dynamic data-centered distributed systems. Although research on the above issues has progressed considerably in the last years, a clear understanding on how to combine data exchange and data integration in peer data management is still missing. This is the subject of the present paper. We start our investigation by first proposing a novel framework for peer data exchange, showing that it is a generalization of the classical data exchange setting. We also present algorithms for all the relevant data exchange tasks, and show that they can all be done in polynomial time with respect to data complexity. Based on the motivation that typical mappings and integrity constraints found in data integration are not captured by peer data exchange, we extend the framework to incorporate these features. One of the main difficulties is that the constraints of this new class are not amenable to materialization. We address this issue by resorting to a suitable combination of virtual and materialized data exchange, showing that the resulting framework is a generalization of both classical data exchange and classical data integration, and that the new setting incorporates the most expressive types of mapping and constraints considered in the two contexts. Finally, we present algorithms for all the relevant data management tasks also in the new setting, and show that, again, their data complexity is polynomial.

was held in December 2008 near Tokyo, Japan. The meeting brought together researchers and practitioners from a variety of subdisciplines of computer science to share research efforts and help create a new community. In this report, we survey the state of the art and summarize the technical presentations delivered at the meeting. We also describe some insights gathered from our discussions and introduce a new effort to establish a benchmark for bidirectional transformations. 1

Data exchange deals with the following problem: given an instance over a source schema, a specification of the relationship between the source and the target, and dependencies on the target, construct an instance over a target schema that satisfies the given relationships and dependencies. Recently—for data exchange settings without target dependencies—Libkin (PODS’06) introduced a new concept of solutions based on the closed world assumption (so called CWA-solutions), and showed that, in some respects, this new notion behaves better than the standard notion of solutions considered in previous papers on data exchange. The present paper extends Libkin’s notion of CWA-solutions to data exchange settings with target dependencies. We show that, when restricting attention to data exchange settings with weakly acyclic target dependencies, this new notion behaves similarly as before: the core is the unique “minimal ” CWA-solution, and computing CWA-solutions as well as certain answers to positive queries is possible in polynomial time and can be PTIME-hard. However, there may be more than one “maximal ” CWA-solution. And going beyond the class of positive queries, we obtain that there are conjunctive queries with (just) one inequality, for which evaluating the certain answers is co-NP-hard. Finally, we consider the Existence-of-CWA-Solutions problem: while the problem is tractable for data exchange settings with weakly acyclic target dependencies, it turns out to be undecidable for general data exchange settings. As a consequence, we obtain that also the Existence-of-Universal-Solutions problem is undecidable in general.

This is a survey of algorithms, complexity results, and general solution techniques for efficiently processing queries on tree-structured data. I focus on query languages that compute nodes or tuples of nodes – conjunctive queries, first-order queries, datalog, and XPath. I also point out a number of connections among previous results that have not been observed before. The techniques belong to five groups: 1. employing orders on the nodes of the tree for efficient labeling schemes and structural joins, 2. linear-time algorithms for evaluating Horn-SAT (the datalog technique), 3. structural decomposition techniques for queries, 4. query rewriting, and 5. holistic query processing techniques that can be explained using ideas from constraint satisfaction. 1

We study models of incomplete information for XML, their computational properties, and query answering. While our approach is motivated by the study of relational incompleteness, incomplete information in XML documents may appear not only as null values but also as missing structural information. Our goal is to provide a classification of incomplete descriptions of XML documents, and separate features- or groups of features- that lead to hard computational problems from those that admit efficient algorithms. Our classification of incomplete information is based on the combination of null values with partial structural descriptions of documents. The key computational problems we consider are consistency of partial descriptions, representability of complete documents by incomplete ones, and query answering. We show how factors such as schema information, the presence of node ids, and missing structural information affect the complexity of these main computational problems, and find robust classes of incomplete XML descriptions that permit tractable query evaluation.

Abstract: Schema mapping techniques for data exchange have become popular and useful tools both in research and industry. A schema mapping relates a source schema with a target schema via correspondences, which are specified by a domain expert possibly supported by automated schema matching algorithms. The set of correspondences, i.e., the mapping, is interpreted as a data transformation usually expressed as a query. These queries transform data from the source schema to conform to the target schema. They can be used to materialize data at the target or used as views in a virtually integrated system. We present a classification of mapping situations that can occur when mapping between two relational or nested (XML) schemata. Our classification takes into consideration 1:1 and n:m correspondences, attribute-level and higher-level mappings, and special constructs, such as choice constraints, cardinality constraints, and data types. Based on this classification, we have developed a general suite of schemata, data, and correspondences to test the ability of tools to cope with the different mapping situations. We evaluated several commercial and research tools that support the definition