Reinhard Pichler

The complexity of XPath query evaluation

In this paper, we study the precise complexity of XPath 1.0 query processing. Even though heavily used by its incorporation into a variety of XML-related standards, the precise cost of evaluating an XPath query is not yet wellunderstood. The first polynomial-time algorithm for XPath processing (with respect to combined complexity) was proposed only recently, and even to this day all major XPath engines take time exponential in the size of the input queries. From the standpoint of theory, the precise complexity of XPath query evaluation is open, and it is thus unknown whether the query evaluation problem can be parallelized.In this work, we show that both the data complexity and the query complexity of XPath 1.0 fall into lower (highly parallelizable) complexity classes, but that the combined complexity is PTIME-hard. Subsequently, we study the sources of this hardness and identify a large and practically important fragment of XPath 1.0 for which the combined complexity is LOGCFL-complete and, therefore, in the highly parallelizable complexity class NC2.

XPath query evaluation: improving time and space efficiency

Contemporary XPath query engines evaluate queries in time exponential in the sizes of input queries, a fact that has gone unnoticed for a long time. Recently, the first main-memory evaluation algorithm for XPath 1.0 with polynomial time combined complexity, i.e., which runs in polynomial time both with respect to the size of the data and the queries, has been published (cf. [G. Gottlob, et al., (2002)]. We present several important improvements and extensions of that work, including new XPath processing algorithms with improved time and space efficiency. Moreover, we define a very large and practically relevant fragment of XPath for which a further optimized form of query evaluation is possible. Apart from its immediate relevance for XPath query processing, our work also sheds new light at those features of XPath 1.0 which are most costly relative to their practical usefulness.

Quality-aware service-oriented data integration: requirements, state of the art and open challenges

With a multitude of data sources available online, data consumers might find it hard to select the best combination of sources for their needs. Aspects such as price, licensing, service and data quality play a major role in selecting data sources. We therefore advocate qualityaware data services as a natural data source model for complex data integration tasks and mash-ups. This paper focuses on requirements, state of the art, and the main research challenges on the way to the realization of such services.

Towards fixed-parameter tractable algorithms for abstract argumentation

Abstract argumentation frameworks have received a lot of interest in recent years. Most computational problems in this area are intractable but several tractable fragments have been identified. In particular, Dunne showed that many problems can be solved in linear time for argumentation frameworks of bounded tree-width. However, these tractability results, which were obtained via Courcelle@?s Theorem, do not directly lead to efficient algorithms. The goal of this paper is to turn the theoretical tractability results into efficient algorithms and to explore the potential of directed notions of tree-width for defining larger tractable fragments. As a by-product, we will sharpen some known complexity results.

Normalization and optimization of schema mappings

Schema mappings are high-level specifications that describe the relationship between two database schemas. They are an important tool in several areas of database research, notably in data integration and data exchange. However, a concrete theory of schema mapping optimization including the formulation of optimality criteria and the construction of algorithms for computing optimal schema mappings is completely lacking to date. The goal of this work is to fill this gap. We start by presenting a system of rewrite rules to minimize sets of source-to-target tuple-generating dependencies (st-tgds, for short). Moreover, we show that the result of this minimization is unique up to variable renaming. Hence, our optimization also yields a schema mapping normalization. By appropriately extending our rewrite rule system, we also provide a normalization of schema mappings containing equality-generating target-dependencies (egds). An important application of such a normalization is in the area of defining the semantics of query answering in data exchange, since several definitions in this area depend on the concrete syntactic representation of the st-tgds. This is, in particular, the case for queries with negated atoms and for aggregate queries. The normalization of schema mappings allows us to eliminate the effect of the concrete syntactic representation of the st-tgds from the semantics of query answering. We discuss in detail how our results can be fruitfully applied to aggregate queries.

XPath processing in a nutshell

We provide a concise yet complete formal definition of the semantics of XPath 1 and summarize e cient algorithms for processing queries in this language. Our presentation is intended both for the reader who is looking for a short but comprehensive formal account of XPath as well as the software developer in need of material that facilitates the rapid implementation of XPath engines.

Working with arms: Complexity results on atomic representations of Herbrand models

An Atomic Representation of a Herbrand Model (ARM) is a finite set of (not necessarily ground) atoms over a given Herbrand universe. Each ARM represents a possibly infinite Herbrand interpretation. This concept has emerged independently in different branches of Computer Science as a natural and useful generalization of the concept of finite Herbrand interpretation. It was shown that several recursively decidable problems on finite Herbrand models (or interpretations) remain decidable on ARMs. The following problems are essential when working with ARMs: Deciding the equivalence of two ARMs, deciding subsumption between ARMS, and evaluating clauses over ARMS. These problems were shown to be decidable, but their computational complexity has remained obscure so far. The previously published decision algorithms require exponential space. In spite of this, by developing new decision procedures, we are able to prove that all mentioned problems are coNP-complete.

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.

Belief revision within fragments of propositional logic

Belief revision has been extensively studied in the framework of propositional logic, but just recently revision within fragments of propositional logic has gained attention. Hereby it is not only the belief set and the revision formula which are given within a certain language fragment, but also the result of the revision has to be located in the same fragment. So far, research in this direction has been mainly devoted to the Horn fragment of classical logic. In this work, we present a general approach to define new revision operators derived from known operators (as for instance, Satohs and Dalals revision operators), such that the result of the revision remains in the fragment under consideration. Our approach is not limited to the Horn case but applicable to any fragment of propositional logic where the models of the formulas are closed under a Boolean function. Thus we are able to uniformly treat cases as dual-Horn, Krom and affine formulas, as well.

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.