Marcelo Arenas

Consistent query answers in inconsistent databases

In this paper we consider the problem of the logical characterization of the notion of consistent answer in a relational database that may violate given integrity constraints. This notion is captured in terms of the possible repaired versions of the database. A method for computing consistent answers is given and its soundness and completeness (for some classes of constraints and queries) proved. The method is based on an iterative procedure whose termination for several classes of constraints is proved as well.

Mapping data in peer-to-peer systems: semantics and algorithmic issues

We consider the problem of mapping data in peer-to-peer data-sharing systems. Such systems often rely on the use of mapping tables listing pairs of corresponding values to search for data residing in different peers. In this paper, we address semantic and algorithmic issues related to the use of mapping tables. We begin by arguing why mapping tables are appropriate for data mapping in a peer-to-peer environment. We discuss alternative semantics for these tables and we present a language that allows the user to specify mapping tables under different semantics. Then, we show that by treating mapping tables as constraints (called mapping constraints) on the exchange of information between peers it is possible to reason about them. We motivate why reasoning capabilities are needed to manage mapping tables and show the importance of inferring new mapping tables from existing ones. We study the complexity of this problem and we propose an efficient algorithm for its solution. Finally, we present an implementation along with experimental results that show that mapping tables may be managed efficiently in practice.

The hyperion project: from data integration to data coordination

We present an architecture and a set of challenges for peer database management systems. These systems team up to build a network of nodes (peers) that coordinate at run time most of the typical DBMS tasks such as the querying, updating, and sharing of data. Such a network works in a way similar to conventional multidatabases. Conventional multidatabase systems are founded on key concepts such as those of a global schema, central administrative authority, data integration, global access to multiple databases, permanent participation of databases, etc. Instead, our proposal assumes total absence of any central authority or control, no global schema, transient participation of peer databases, and constantly evolving coordination rules among databases. In this work, we describe the status of the Hyperion project, present our current solutions, and outline remaining research issues.

Answer sets for consistent query answering in inconsistent databases

A relational database is inconsistent if it does not satisfy a given set of integrity constraints. Nevertheless, it is likely that most of the data in it is consistent with the constraints. In this paper we apply logic programming based on answer sets to the problem of retrieving consistent information from a possibly inconsistent database. Since consistent information persists from the original database to every of its minimal repairs, the approach is based on a specification of database repairs using disjunctive logic programs with exceptions, whose answer set semantics can be represented and computed by systems that implement stable model semantics. These programs allow us to declare persistence by default of data from the original instance to the repairs; and changes to restore consistency, by exceptions. We concentrate mainly on logic programs for binary integrity constraints, among which we find most of the integrity constraints found in practice.

nSPARQL: A navigational language for RDF

Navigational features have been largely recognized as fundamental for graph database query languages. This fact has motivated several authors to propose RDF query languages with navigational capabilities. In this paper, we propose the query language nSPARQL that uses nested regular expressions to navigate RDF data. We study some of the fundamental properties of nSPARQL and nested regular expressions concerning expressiveness and complexity of evaluation. Regarding expressiveness, we show that nSPARQL is expressive enough to answer queries considering the semantics of the RDFS vocabulary by directly traversing the input graph. We also show that nesting is necessary in nSPARQL to obtain this last result, and we study the expressiveness of the combination of nested regular expressions and SPARQL operators. Regarding complexity of evaluation, we prove that given an RDF graph G and a nested regular expression E, this problem can be solved in time O(|G|@?|E|).

XML data exchange: consistency and query answering

Data exchange is the problem of finding an instance of a target schema, given an instance of a source schema and a specification of the relationship between the source and the target. Theoretical foundations of data exchange have recently been investigated for relational data.In this paper, we start looking into the basic properties of XML data exchange, that is, restructuring of XML documents that conform to a source DTD under a target DTD, and answering queries written over the target schema. We define XML data exchange settings in which source-to-target dependencies refer to the hierarchical structure of the data. Combining DTDs and dependencies makes some XML data exchange settings inconsistent. We investigate the consistency problem and determine its exact complexity.We then move to query answering, and prove a dichotomy theorem that classifies data exchange settings into those over which query answering is tractable, and those over which it is coNP-complete, depending on classes of regular expressions used in DTDs. Furthermore, for all tractable cases we give polynomial-time algorithms that compute target XML documents over which queries can be answered.

A normal form for XML documents

This paper takes a first step towards the design and normalization theory for XML documents. We show that, like relational databases, XML documents may contain redundant information, and may be prone to update anomalies. Furthermore, such problems are caused by certain functional dependencies among paths in the document. Our goal is to find a way of converting an arbitrary DTD into a well-designed one, that avoids these problems. We first introduce the concept of a functional dependency for XML, and define its semantics via a relational representation of XML. We then define an XML normal form, XNF, that avoids update anomalies and redundancies. We study its properties and show that it generalizes BCNF and a normal form for nested relations when those are appropriately coded as XML documents. Finally, we present a lossless algorithm for converting any DTD into one in XNF.

Scalar aggregation in inconsistent databases

We consider here scalar aggregation queries in databases that may violate a given set of functional dependencies. We define consistent answers to such queries to be greatest-lowest/least-upper bounds on the value of the scalar function across all (minimal) repairs of the database. We show how to compute such answers. We provide a complete characterization of the computational complexity of this problem. We also show how tractability can be improved in several special cases (one involves a novel application of Boyce-Codd Normal Form) and present a practical hybrid query evaluation method.

XML data exchange: Consistency and query answering

Data exchange is the problem of finding an instance of a target schema, given an instance of a source schema and a specification of the relationship between the source and the target. Theoretical foundations of data exchange have recently been investigated for relational data. In this article, we start looking into the basic properties of XML data exchange, that is, restructuring of XML documents that conform to a source DTD under a target DTD, and answering queries written over the target schema. We define XML data exchange settings in which source-to-target dependencies refer to the hierarchical structure of the data. Combining DTDs and dependencies makes some XML data exchange settings inconsistent. We investigate the consistency problem and determine its exact complexity. We then move to query answering, and prove a dichotomy theorem that classifies data exchange settings into those over which query answering is tractable, and those over which it is coNP-complete, depending on classes of regular expressions used in DTDs. Furthermore, for all tractable cases we give polynomial-time algorithms that compute target XML documents over which queries can be answered.

Querying semantic web data with SPARQL

The Semantic Web is the initiative of the W3C to make information on the Web readable not only by humans but also by machines. RDF is the data model for Semantic Web data, and SPARQL is the standard query language for this data model. In the last ten years, we have witnessed a constant growth in the amount of RDF data available on the Web, which have motivated the theoretical study of some fundamental aspects of SPARQL and the development of efficient mechanisms for implementing this query language. Some of the distinctive features of RDF have made the study and implementation of SPARQL challenging. First, as opposed to usual database applications, the semantics of RDF is open world, making RDF databases inherently incomplete. Thus, one usually obtains partial answers when querying RDF with SPARQL, and the possibility of adding optional information if present is a crucial feature of SPARQL. Second, RDF databases have a graph structure and are interlinked, thus making graph navigational capabilities a necessary component of SPARQL. Last, but not least, SPARQL has to work at Web scale! RDF and SPARQL have attracted interest from the database community. However, we think that this community has much more to say about these technologies, and, in particular, about the fundamental database problems that need to be solved in order to provide solid foundations for the development of these technologies. In this paper, we survey some of the main results about the theory of RDF and SPARQL putting emphasis on some research opportunities for the database community.