Juan L. Reutter

Querying graph patterns

Graph data appears in a variety of application domains, and many uses of it, such as querying, matching, and transforming data, naturally result in incompletely specified graph data, i.e., graph patterns. While queries need to be posed against such data, techniques for querying patterns are generally lacking, and properties of such queries are not well understood. Our goal is to study the basics of querying graph patterns. We first identify key features of patterns, such as node and label variables and edges specified by regular expressions, and define a classification of patterns based on them. We then study standard graph queries on graph patterns, and give precise characterizations of both data and combined complexity for each class of patterns. If complexity is high, we do further analysis of features that lead to intractability, as well as lower complexity restrictions. We introduce a new automata model for query answering with two modes of acceptance: one captures queries returning nodes, and the other queries returning paths. We study properties of such automata, and the key computational tasks associated with them. Finally, we provide additional restrictions for tractability, and show that some intractable cases can be naturally cast as instances of constraint satisfaction problem.

Trial for RDF: adapting graph query languages for RDF data

Querying RDF data is viewed as one of the main applications of graph query languages, and yet the standard model of graph databases -- essentially labeled graphs -- is different from the triples-based model of RDF. While encodings of RDF databases into graph data exist, we show that even the most natural ones are bound to lose some functionality when used in conjunction with graph query languages. The solution is to work directly with triples, but then many properties taken for granted in the graph database context (e.g., reachability) lose their natural meaning. Our goal is to introduce languages that work directly over triples and are closed, i.e., they produce sets of triples, rather than graphs. Our basic language is called TriAL, or Triple Algebra: it guarantees closure properties by replacing the product with a family of join operations. We extend TriAL with recursion, and explain why such an extension is more intricate for triples than for graphs. We present a declarative language, namely a fragment of datalog, capturing the recursive algebra. For both languages, the combined complexity of query evaluation is given by low-degree polynomials. We compare our languages with relational languages, such as finite-variable logics, and previously studied graph query languages such as adaptations of XPath, regular path queries, and nested regular expressions; many of these languages are subsumed by the recursive triple algebra. We also provide examples of the usefulness of TriAL in querying graph and RDF data.

Composition and inversion of schema mappings

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 data integration. The research on this area has mainly focused on performing these tasks. However, as Bernstein pointed out [7], many information-system problems involve not only the design and integration of complex application artifacts, but also their subsequent manipulation. Driven by this consideration, Bernstein proposed in [7] a general framework for managing schema mappings. In this framework, mappings are usually specified in a logical language, and high-level algebraic operators are used to manipulate them [7, 16, 33, 12, 8]. Two of the most fundamental operators in this framework are the composition and inversion of schema mappings. Intuitively, the composition can be described as follows. Given a mapping M1 from a schema A to a schema B, and a mapping M2 from B to a schema E, the composition of M1 and M2 is a new mapping that describes the relationship between schemas A and E. This new mapping must be semantically consistent with the relationships previously established by M1 and M2. On the other hand, an inverse of M1 is a new mapping that describes the reverse relationship from B to A, and is semantically consistent with M1. In practical scenarios, the composition and inversion of schema mappings can have several applications. In a data exchange context [13], if a mapping M is used to exchange data from a source to a target schema, an inverse of M can be used to exchange the data back to the source, thus reversing the application of M. As a second application, consider a peer-data management system (PDMS) [10, 24]. In a PDMS, a peer can act as a data source, a mediator, or both, and the system relates peers

SPARQL with Property Paths

The original SPARQL proposal was often criticized for its inability to navigate through the structure of RDF documents. For this reason property paths were introduced in SPARQL 1.1, but up to date there are no theoretical studies examining how their addition to the language affects main computational tasks such as query evaluation, query containment, and query subsumption. In this paper we tackle all of these problems and show that although the addition of property paths has no impact on query evaluation, they do make the containment and subsumption problems substantially more difficult.

Data exchange beyond complete data

In the traditional data exchange setting, source instances are restricted to be complete in the sense that every fact is either true or false in these instances. Although natural for a typical database translation scenario, this restriction is gradually becoming an impediment to the development of a wide range of applications that need to exchange objects that admit several interpretations. In particular, we are motivated by two specific applications that go beyond the usual data exchange scenario: exchanging incomplete information and exchanging knowledge bases. In this paper, we propose a general framework for data exchange that can deal with these two applications. More specifically, we address the problem of exchanging information given by representation systems, which are essentially finite descriptions of (possibly infinite) sets of complete instances. We make use of the classical semantics of mappings specified by sets of logical sentences to give a meaningful semantics to the notion of exchanging representatives, from which the standard notions of solution, space of solutions, and universal solution naturally arise. We also introduce the notion of strong representation system for a class of mappings, that resembles the concept of strong representation system for a query language. We show the robustness of our proposal by applying it to the two applications mentioned above: exchanging incomplete information and exchanging knowledge bases, which are both instantiations of the exchanging problem for representation systems. We study these two applications in detail, presenting results regarding expressiveness, query answering and complexity of computing solutions, and also algorithms to materialize solutions.

Querying Regular Graph Patterns

Graph data appears in a variety of application domains, and many uses of it, such as querying, matching, and transforming data, naturally result in incompletely specified graph data, that is, graph patterns. While queries need to be posed against such data, techniques for querying patterns are generally lacking, and properties of such queries are not well understood. Our goal is to study the basics of querying graph patterns. The key features of patterns we consider here are node and label variables and edges specified by regular expressions. We provide a classification of patterns, and study standard graph queries on graph patterns. We give precise characterizations of both data and combined complexity for each class of patterns. If complexity is high, we do further analysis of features that lead to intractability, as well as lower-complexity restrictions. Since our patterns are based on regular expressions, query answering for them can be captured by a new automata model. These automata have two modes of acceptance: one captures queries returning nodes, and the other queries returning paths. We study properties of such automata, and the key computational tasks associated with them. Finally, we provide additional restrictions for tractability, and show that some intractable cases can be naturally cast as instances of constraint satisfaction problems.

Foundations of schema mapping management

In the last few years, a lot of attention has been paid to the specification and subsequent manipulation of schema mappings, a problem which is of fundamental importance in metadata management. There have been many achievements in this area, and semantics have been defined for operators on schema mappings such as composition and inverse. However, little research has been pursued towards providing formal tools to compare schema mappings, in terms of their ability to transfer data and avoid storing redundant information, which has hampered the development of foundations for more complex operators as many of them involve these notions. In this paper, we address the problem of providing foundations for metadata management by developing an order to compare the amount of information transferred by schema mappings. From this order we derive several other criteria to compare mappings, we provide tools to deal with these criteria, and we show their usefulness in defining and studying schema mapping operators. More precisely, we show how the machinery developed can be used to study the extract and merge operators, that have been identified as fundamental for the development of a metadata management framework. We also use our machinery to provide simpler proofs for some fundamental results regarding the inverse operator, and we give an effective characterization for the decidability of the well-known schema evolution problem.

Inverting schema mappings: bridging the gap between theory and practice

The inversion of schema mappings has been identified as one of the fundamental operators for the development of a general framework for metadata management. In fact, during the last years three alternative notions of inversion for schema mappings have been proposed (Fagin-inverse [10], quasi-inverse [14] and maximum recovery [2]). However, the procedures that have been developed for computing these operators have some features that limit their practical applicability. First, these algorithms work in exponential time and produce inverse mappings of exponential size. Second, these algorithms express inverses in some mappings languages which include features that are difficult to use in practice. A typical example is the use of disjunction in the conclusion of the mapping rules, which makes the process of exchanging data much more complicated. In this paper, we propose solutions for the two problems mentioned above. First, we provide a polynomial time algorithm that computes the three inverse operators mentioned above given a mapping specified by a set of tuple-generating dependencies (tgds). This algorithm uses an output mapping language that can express these three operators in a compact way and, in fact, can compute inverses for a much larger class of mappings. Unfortunately, it has already been proved that this type of mapping languages has to include some features that are difficult to use in practice and, hence, this is also the case for our output mapping language. Thus, as our second contribution, we propose a new and natural notion of inversion that overcomes this limitation. In particular, every mapping specified by a set of tgds admits an inverse under this new notion that can be expressed in a mapping language that slightly extends tgds, and that has the same good properties for data exchange as tgds. Finally, as our last contribution, we provide an algorithm for computing such inverses.

Query languages for data exchange: beyond unions of conjunctive queries

The class of unions of conjunctive queries (UCQ) has been shown to be particularly well-behaved for data exchange; its certain answers can be computed in polynomial time (in terms of data complexity). However, this is not the only class with this property; the certain answers to any Datalog program can also can be computed in polynomial time. The problem is that both UCQ and Datalog do not allow negated atoms, as adding an unrestricted form of negation to these languages yields to intractability. In this paper, we propose a language called DatalogC(≠) that extends Datalog with a restricted form of negation, and study some of its fundamental properties. In particular, we show that the certain answers to a DatalogC(≠) program can be computed in polynomial time (in terms of data complexity), and that every union of conjunctive queries with at most one inequality or negated relational atom per disjunct, can be efficiently rewritten as a DatalogC(≠) program in the context of data exchange. Furthermore, we show that this is also the case for a syntactic restriction of the class of unions of conjunctive queries with at most two inequalities per disjunct. This syntactic restriction is given by two conditions that are optimal, in the sense that computing certain answers becomes intractable if one removes any of them. Finally, we provide a thorough analysis of the combined complexity of computing certain answers to DatalogC(≠) programs and other related query languages. In particular, we show that this problem is Exptime-complete for DatalogC(≠), even if one restricts to conjunctive queries with single inequalities, which is a fragment of DatalogC(≠) by the result mentioned above. Furthermore, we show that the combined complexity is CoNexptime-complete for the case of conjunctive queries with k inequalities, for every k ≥ 2.

Schema mappings and data exchange for graph databases

Data exchange and schema mapping management have received little attention so far in the graph database scenario, and tools developed in this context for relational databases have significant drawbacks in the context of graph-structured data. In this paper we embark on the study of interoperability issues for graph databases, including schema mappings, data exchange and certain answers computation. We start by analyzing different possibilities for specifying mappings in graph databases. Our mapping languages are based on the most typical graph databases queries, ranging from regular path queries to conjunctions of nested regular expressions. They subsume all previously considered mapping languages, and let one express many data exchange scenarios in the graph database context. We study the problems of materializing solutions and query answering, in particular, the problem of computing universal representatives and certain answers for various classes of mappings. We show that both problems are difficult with respect to combined complexity, and that for the latter problem, even data complexity is high for some very simple mappings and queries. We then identify relevant classes of mappings and queries for which the problems of materializing solutions and query answering can be solved efficiently.