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

A schema mapping is a specification that describes how data from a source schema is to be mapped to a target schema. Schema mappings have proved to be essential for data-interoperability tasks such as data exchange and

In XML data exchange, a schema mapping specifies rules for restructuring a source document under the target schema, and queries over the target document must be answered in a way consistent with the source information. Mapping rules and queries in this scenario are typically based on various kinds of tree patterns. Patterns with downward navigation have been studied, and tractable classes of mappings and queries have been isolated. In this paper we extend schema mappings and queries with general tree patterns that include horizontal navigation and data-value comparisons, and study their impact on the tractability of the query answering problem. Our main results state that, in the nutshell, extending the tractable cases for downward patterns with expressive schema mappings is harmless, but adding new features to queries quickly leads to intractability even for very simple schema mapping. 1.

The notion of certain answers arises when one queries incompletely specified databases, e.g., in data integration and exchange scenarios, or databases with missing information. While in the relational case this notion is well understood, there is no natural analog of it for XML queries that return documents. We develop an approach to defining certain answers for such XML queries, and apply it in the settings of incomplete information and XML data exchange. We first revisit the relational case, and show how to present the key concepts related to certain answers in a new model-theoretic language. This new approach naturally extends to XML. We prove a number of generic, application-independent results about computability and complexity of certain answers produced by it. We then turn our attention to a pattern-based XML query language with trees as outputs, and present a technique for computing certain answers that relies on the notion of a basis of a set of trees. We show how to compute such bases for documents with nulls and for documents arising in data exchange scenarios, and provide complexity bounds. While in general complexity of query answering in XML data exchange could be high, we exhibit a natural class of XML schema mappings for which not only query answering, but also many static analysis problems can be solved efficiently.

building, solution existence The task of XML data exchange is to restructure a document conforming to a source schema under a target schema according to certain mapping rules. The rules are typically expressed as source-to-target dependencies using various kinds of patterns, involving horizontal and vertical navigation, as well as data comparisons. The target schema imposes complex conditions on the structure of solutions, possibly inconsistent with the mapping rules. In consequence, for some source documents there may be no solutions. We investigate three problems: deciding if all documents of the source schema can be mapped to a document of the target schema (absolute consistency), deciding if a given document of the source schema can be mapped (solution existence), and constructing a solution for a given source document (solution building). We show that the complexity of absolute consistency is rather high in general, but within the polynomial hierarchy for bounded depth schemas. The combined complexity of solution existence and solution building behaves similarly, but the data complexity turns out to be very low. In addition to this we show that even for much more expressive mapping rules, based on MSO definable queries, absolute consistency is decidable and data complexity of solution existence is polynomial.

The task of XML data exchange is to restructure a document conforming to a source schema under a target schema according to certain mapping rules. The rules are typically expressed as source-totarget dependencies using various kinds of patterns, involving horizontal and vertical navigation, as well as data comparisons. The target schema imposes complex conditions on the structure of solutions, possibly inconsistent with the mapping rules. In consequence, for some source documents there may be no solutions. We investigate three problems: deciding if all documents of the source schema can be mapped to a document of the target schema (absolute consistency), deciding if a given document of the source schema can be mapped (solution existence), and constructing a solution for a given source document (solution building). We show that the complexity of absolute consistency is rather high in general, but within the polynomial hierarchy for bounded depth schemas. The combined complexity of solution existence and solution building behaves similarly, but the data complexity turns out to be very low. In addition to this we show that even for much more expressive mapping rules, based on MSO definable queries, absolute consistency is decidable and data complexity of solution existence is polynomial.