On Incomplete XML Documents with Integrity Constraints

Abstract. We consider incomplete specifications of XML documents in the presence of schema information and integrity constraints. We show that integrity constraints such as keys and foreign keys affect consistency of such specifications. We prove that the consistency problem for incomplete specifications with keys and foreign keys can always be solved in NP. We then show a dichotomy result, classifying the complexity of the problem as NP-complete or PTIME, depending on the precise set of features used in incomplete descriptions.

Optimal Joins Using Compact Data Structures

Worst-case optimal join algorithms have gained a lot of attention in the database literature. We now count with several algorithms that are optimal in the worst case, and many of them have been implemented and validated in practice. However, the implementation of these algorithms often requires an enhanced indexing structure: to achieve optimality we either need to build completely new indexes, or we must populate the database with several instantiations of indexes such as B+-trees. Either way, this means spending an extra amount of storage space that may be non-negligible. We show that optimal algorithms can be obtained directly from a representation that regards the relations as point sets in variable-dimensional grids, without the need of extra storage. Our representation is a compact quadtree for the static indexes, and a dynamic quadtree sharing subtrees (which we dub a qdag) for intermediate results. We develop a compositional algorithm to process full join queries under this representation, and show that the running time of this algorithm is worst-case optimal in data complexity. Remarkably, we can extend our framework to evaluate more expressive queries from relational algebra by introducing a lazy version of qdags (lqdags). Once again, we can show that the running time of our algorithms is worst-case optimal

CONSTRUCT Queries in SPARQL

SPARQL has become the most popular language for querying RDF datasets, the standard data model for representing information in the Web. This query language has received a good deal of attention in the last few years: two versions of W3C standards have been issued, several SPARQL query engines have been deployed, and important theoretical foundations have been laid. However, many fundamental aspects of SPARQL queries are not yet fully understood. To this end, it is crucial to understand the correspondence between SPARQL and well-developed frameworks like relational algebra or first order logic. But one of the main obstacles on the way to such understanding is the fact that the well-studied fragments of SPARQL do not produce RDF as output. In this paper we embark on the study of SPARQL CONSTRUCT queries, that is, queries which output RDF graphs. This class of queries takes rightful place in the standards and implementations, but contrary to SELECT queries, it has not yet attracted a worth-while theoretical research. Under this framework we are able to establish a strong connection between SPARQL and well-known logical and database formalisms. In particular, the fragment which does not allow for blank nodes in output templates corresponds to first order queries, its well-designed sub-fragment corresponds to positive first order queries, and the general language can be re-stated as a data exchange setting. These correspondences allow us to conclude that the general language is not composable, but the aforementioned blank-free fragments are. Finally, we enrich SPARQL with a recursion operator and establish fundamental properties of this extension

Graph Patterns: Structure, Query Answering and Applications in Schema Mappings and Formal Language Theory

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. Queries need to be posed against such data, but techniques for querying patterns are generally lacking, and even simple properties of graph patterns, such as the languages needed to specify them, are not well understood. In this dissertation we present several contributions in the study of graph patterns. We analyze how to query them and how to use them as queries. We also analyze some of their applications in two different contexts: schema mapping specification and data exchange for graph databases, and formal language theory. 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. Next we study how to answer standard graph queries over 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 that guarantee tractability. We then turn to the the study of schema mappings for graph databases. As for relational and XML databases, our mapping languages are based on patterns. They subsume all previously considered mapping languages for graph databases, and are capable of expressing many data exchange scenarios in the graph database context. We study the problems of materializing solutions and query answering for data exchange under these mappings, analyze their complexity, and identify relevant classes of mappings and queries for which these problems can be solved efficiently. We also introduce a new model of automata that is based on graph patterns, and define two modes of acceptance for them. We show that this model has applications not only in graph databases but in several other contexts. We study the basic properties of such automata, and the key computational tasks associated with them

Regular Queries on Graph Databases

Graph databases are currently one of the most popular paradigms for storing data. One of the key conceptual differences between graph and relational databases is the focus on navigational queries that ask whether some nodes are connected by paths satisfying certain restrictions. This focus has driven the definition of several different query languages and the subsequent study of their fundamental properties. We define the graph query language of Regular Queries, which is a natural extension of unions of conjunctive 2-way regular path queries (UC2RPQs) and unions of conjunctive nested 2-way regular path queries (UCN2RPQs). Regular queries allow expressing complex regular patterns between nodes. We formalize regular queries as nonrecursive Datalog programs with transitive closure rules. This language has been previously considered, but its algorithmic properties are not well understood. Our main contribution is to show elementary tight bounds for the containment problem for regular queries. Specifically, we show that this problem is 2EXPSPACE-complete. For all extensions of regular queries known to date, the containment problem turns out to be non-elementary. Together with the fact that evaluating regular queries is not harder than evaluating UCN2RPQs, our results show that regular queries achieve a good balance between expressiveness and complexity, and constitute a well-behaved class that deserves further investigation

Classification of annotation semirings over containment of conjunctive queries

Funding: This work is supported under SOCIAM: The Theory and Practice of Social Machines, a project funded by the UK Engineering and Physical Sciences Research Council (EPSRC) under grant number EP/J017728/1. This work was also supported by FET-Open Project FoX, grant agreement 233599; EPSRC grants EP/F028288/1, G049165 and J015377; and the Laboratory for Foundations of Computer Science.We study the problem of query containment of conjunctive queries over annotated databases. Annotations are typically attached to tuples and represent metadata, such as probability, multiplicity, comments, or provenance. It is usually assumed that annotations are drawn from a commutative semiring. Such databases pose new challenges in query optimization, since many related fundamental tasks, such as query containment, have to be reconsidered in the presence of propagation of annotations. We axiomatize several classes of semirings for each of which containment of conjunctive queries is equivalent to existence of a particular type of homomorphism. For each of these types, we also specify all semirings for which existence of a corresponding homomorphism is a sufficient (or necessary) condition for the containment. We develop new decision procedures for containment for some semirings which are not in any of these classes. This generalizes and systematizes previous approaches.PostprintPeer reviewe

Property Paths over Linked Data: Can it be Done and How to Start?

Abstract. One of the advantages that Linked Data offers over the classical database setting is the ability to connect and navigate through different datasets. At the moment the standard mechanism for exploring navigational properties of the Semantic Web data are SPARQL property paths. However, the semantics of property paths is only defined assuming one evaluates them over a single local database, and it is still not clear what is the correct way to implement them over the Web of Linked Data, nor if this is even feasible. In this paper we explore this topic in more depth and gauge the merits of different approaches of executing property paths over Linked Data. To this end we test how property paths perform if the Linked Data is assumed to be available locally, through endpoints, or if it is accessed directly through dereferencing IRIs