Sebastian Skritek

Containment and equivalence of well-designed SPARQL

Query containment and query equivalence constitute important computational problems in the context of static query analysis and optimization. While these problems have been intensively studied for fragments of relational calculus, almost no works exist for the semantic web query language SPARQL. In this paper, we carry out a comprehensive complexity analysis of containment and equivalence for several fragments of SPARQL: we start with the fundamental fragment of well-designed SPARQL restricted to the AND and OPTIONAL operator. We then study basic extensions in the form of the UNION operator and/or projection. The results obtained range from NP-completeness to undecidability.

Tractable counting of the answers to conjunctive queries

Conjunctive queries (CQs) are one of the most fundamental forms of database queries. In general, the evaluation of CQs is NP-complete. Consequently, there has been an intensive search for tractable fragments. In this paper, we want to initiate a systematic search for tractable fragments of the counting problem of CQs, i.e., the problem of counting the answers to a CQ. We prove several new tractability and intractability results by starting with acyclic conjunctive queries and generalising these results to CQs of bounded hypertree-width. We also extend our study to the counting problem of unions of CQs.

Efficient Evaluation and Approximation of Well-designed Pattern Trees

Conjunctive queries (CQs) fail to provide an answer when the pattern described by the query does not exactly match the data. CQs might thus be too restrictive as a querying mechanism when data is semistructured or incomplete. The semantic web therefore provides a formalism - known as well-designed pattern trees (WDPTs) - that tackles this problem: WDPTs allow us to match patterns over the data, if available, but do not fail to give an answer otherwise. Here we abstract away the specifics of semantic web applications and study WDPTs over arbitrary relational schemas. Our language properly subsumes the class of CQs. Hence, WDPT evaluation is intractable. We identify structural proper ties of WDPTs that lead to tractability of various variants of the evaluation problem. For checking if a WDPT is equivalent to one in our tractable class, we prove 2EXPTIME-membership. As a corollary, we obtain fixed-parameter tractability of (variants of) the evaluation problem. Our techniques also allow us to develop a theory of approximations for WDPTs.

Towards Reconciling SPARQL and Certain Answers

SPARQL entailment regimes are strongly influenced by the big body of works on ontology-based query answering, notably in the area of Description Logics (DLs). However, the semantics of query answering under SPARQL entailment regimes is defined in a more naive and much less expressive way than the certain answer semantics usually adopted in DLs. The goal of this work is to introduce an intuitive certain answer semantics also for SPARQL and to show the feasibility of this approach. For OWL 2 QL entailment, we present algorithms for the evaluation of an interesting fragment of SPARQL (the so-called well-designed SPARQL). Moreover, we show that the complexity of the most fundamental query analysis tasks (such as query containment and equivalence testing) is not negatively affected by the presence of OWL 2 QL entailment under the proposed semantics.

Redundancy elimination on RDF graphs in the presence of rules, constraints, and queries

Based on practical observations on rule-based inference on RDF data, we study the problem of redundancy elimination on RDF graphs in the presence of rules (in the form of Datalog rules) and constraints (in the form of so-called tuple-generating dependencies), as well as with respect to queries (ranging from conjunctive queries up to more complex ones, particularly covering features of SPARQL, such as union, negation, or filters). To this end, we investigate the influence of several problem parameters (like restrictions on the size of the rules, the constraints, and/or the queries) on the complexity of detecting redundancy. The main result of this paper is a fine-grained complexity analysis of both graph and rule minimisation in various settings.

The complexity of evaluating tuple generating dependencies

Dependencies have played an important role in database design for many years. More recently, they have also turned out to be central to data integration and data exchange. In this work we concentrate on tuple generating dependencies (tgds) which enforce the presence of certain tuples in a database instance if certain other tuples are already present. Previous complexity results in data integration and data exchange mainly referred to the data complexity. In this work, we study the query complexity and combined complexity of a fundamental problem related to tgds, namely checking if a given tgd is satisfied by a database instance. We also address an important variant of this problem which deals with updates (by inserts or deletes) of a database: Here we have to check if all previously satisfied tgds are still satisfied after an update. We show that the query complexity and combined complexity of these problems are much higher than the data complexity. However, we also prove sufficient conditions on the tgds to reduce this high complexity.

Complexity of redundancy detection on RDF graphs in the presence of rules, constraints, and queries

Based on practical observations on rule-based inference on RDF data, we study the problem of redundancy detection on RDF graphs in the presence of rules in the form of Datalog rules and constraints, in the form of so-called tuple-generating dependencies, and with respect to queries ranging from conjunctive queries up to more complex ones, particularly covering features of SPARQL, such as union, negation, or filters. To this end, we investigate the influence of several problem parameters like restrictions on the size of the rules, the constraints, and/or the queries on the complexity of detecting redundancy. The main result of this paper is a fine-grained complexity analysis of both graph and rule minimisation in various settings.

On the Complexity of Hard Enumeration Problems

Complexity theory provides a wealth of complexity classes for analyzing the complexity of decision and counting problems. Despite the practical relevance of enumeration problems, the tools provided by complexity theory for this important class of problems are very limited. In particular, complexity classes analogous to the polynomial hierarchy and an appropriate notion of problem reduction are missing. In this work, we lay the foundations for a complexity theory of hard enumeration problems by proposing a hierarchy of complexity classes and by investigating notions of reductions for enumeration problems.

SPAM: a SPARQL analysis and manipulation tool

SQL developers are used to having elaborate tools which help them in writing queries. In contrast, the creation of tools to assist users in the development of SPARQL queries is still in its infancy. In this system demo, we present the SPARQL Analysis and Manipulation (SPAM) tool, which provides help for the development of SPARQL queries. The main features of the SPAM tool comprise an editor with both text and graphical interface, as well as various functions for the static and dynamic analysis of SPARQL queries.

Efficient Evaluation and Static Analysis for Well-Designed Pattern Trees with Projection

Conjunctive queries (CQs) fail to provide an answer when the pattern described by the query does not exactly match the data. CQs might thus be too restrictive as a querying mechanism when data is semistructured or incomplete. The semantic web therefore provides a formalism—known as (projected) well-designed pattern trees (pWDPTs)—that tackles this problem: pWDPTs allow us to formulate queries that match parts of the query over the data if available, but do not ignore answers of the remaining query otherwise. Here we abstract away the specifics of semantic web applications and study pWDPTs over arbitrary relational schemas. Since the language of pWDPTs subsumes CQs, their evaluation problem is intractable. We identify structural properties of pWDPTs that lead to (fixed-parameter) tractability of various variants of the evaluation problem. We also show that checking if a pWDPT is equivalent to one in our tractable class is in 2EXPTIME. As a corollary, we obtain fixed-parameter tractability of evaluation for pWDPTs with such good behavior. Our techniques also allow us to develop a theory of approximations for pWDPTs.