On the Complexity of Enumerating the Answers to Well-designed Pattern Trees

Well-designed pattern trees (wdPTs) have been introduced as an extension of conjunctive queries to allow for partial matching - analogously to the OPTIONAL operator of the semantic web query language SPARQL. Several computational problems of wdPTs have been studied in recent years, such as the evaluation problem in various settings, the counting problem, as well as static analysis tasks including the containment and equivalence problems. Also restrictions needed to achieve tractability of these tasks have been proposed. In contrast, the problem of enumerating the answers to a wdPT has been largely ignored so far. In this work, we embark on a systematic study of the complexity of the enumeration problem of wdPTs. As our main result, we identify several tractable and intractable cases of this problem both from a classical complexity point of view and from a parameterized complexity point of view

Peer Data Management

Peer Data Management (PDM) deals with the management of structured data in unstructured peer-to-peer (P2P) networks. Each peer can store data locally and define relationships between its data and the data provided by other peers. Queries posed to any of the peers are then answered by also considering the information implied by those mappings. The overall goal of PDM is to provide semantically well-founded integration and exchange of heterogeneous and distributed data sources. Unlike traditional data integration systems, peer data management systems (PDMSs) thereby allow for full autonomy of each member and need no central coordinator. The promise of such systems is to provide flexible data integration and exchange at low setup and maintenance costs. However, building such systems raises many challenges. Beside the obvious scalability problem, choosing an appropriate semantics that can deal with arbitrary, even cyclic topologies, data inconsistencies, or updates while at the same time allowing for tractable reasoning has been an area of active research in the last decade. In this survey we provide an overview of the different approaches suggested in the literature to tackle these problems, focusing on appropriate semantics for query answering and data exchange rather than on implementation specific problems

Characterizing Tractability of Simple Well-Designed Pattern Trees with Projection

We study the complexity of evaluating well-designed pattern trees, a query language extending conjunctive queries with the possibility to define parts of the query to be optional. This possibility of optional parts is important for obtaining meaningful results over incomplete data sources as it is common in semantic web settings. Recently, a structural characterization of the classes of well-designed pattern trees that can be evaluated in polynomial time was shown. However, projection - a central feature of many query languages - was not considered in this study. We work towards closing this gap by giving a characterization of all tractable classes of simple well-designed pattern trees with projection (under some common complexity theoretic assumptions). Since well-designed pattern trees correspond to the fragment of well-designed {AND, OPTIONAL}-SPARQL queries this gives a complete description of the tractable classes of queries with projections in this fragment that can be characterized by the underlying graph structures of the queries

Diversity of Answers to Conjunctive Queries

Enumeration problems aim at outputting, without repetition, the set of solutions to a given problem instance. However, outputting the entire solution set may be prohibitively expensive if it is too big. In this case, outputting a small, sufficiently diverse subset of the solutions would be preferable. This leads to the Diverse-version of the original enumeration problem, where the goal is to achieve a certain level d of diversity by selecting k solutions. In this paper, we look at the Diverse-version of the query answering problem for Conjunctive Queries and extensions thereof. That is, we study the problem if it is possible to achieve a certain level d of diversity by selecting k answers to the given query and, in the positive case, to actually compute such k answers.Comment: 34 pages, accepted to ICDT 202

Implementing a Peer Data Management System

Zsfassung in dt. SpracheDer Begriff "Peer Data Management System" (PDMS) bezeichnet einen Ansatz um die Flexibilität von Peer-to-Peer (P2P) Systemen mit der Ausdruckskraft und klar definierten Semantik von Datenbanksystemen zu verbinden. Dabei nimmt man an, dass die Daten auf verschiedenen, unabhängigen Knoten (Peers) verteilt sind. Jeder Peer ermöglicht über ein Peer-Schema Zugriff auf seine Daten und kann - ähnlich wie bei Datenintegration ("Data Integration") und Datenaustausch ("Data Exchange") - Abbildungen fremder Peer-Schemata auf sein eigenes Schema definieren. Im Gegensatz zu Datenintegration, Datenaustausch oder Multidatenbanksystemen benötigen PDMSs jedoch kein globales Schema und somit keine zentrale Kontrollinstanz. Alle Beziehungen werden lokal zwischen jeweils zwei Peers definiert. Da dies im allgemeinen Fall dazu führen kann, dass etwa die Beantwortung einer Abfrage an ein PDMS unentscheidbar wird, wurden in den letzten Jahren verschiedene Ansätze entwickelt um die Entscheidbarkeit typischer Probleme im Bereich der Datenbanken zu erhalten. Deshalb die Topologie des P2P-Netzwerkes einzuschränken widerspricht jedoch der Idee von vollständig autonomen Peers. Eine andere Möglichkeit besteht darin, die Ausdruckskraft der Abbildungen stärker zu beschränken. Basierend auf dieser Idee schlugen De Giacomo et al.2007 ein theoretisches Modell für ein PDMS vor, welches eine beliebige Topologie des P2P Netzwerkes erlaubt und sowohl den klassischen Datenaustausch als auch die klassische Datenintegration als Spezialfälle umfasst. Nach unserem Wissenstand existiert bislang keine Implementierung dieses Ansatzes. Ziel der vorliegenden Arbeit war es die theoretischen Grundlagen von PDMSs zu untersuchen und einen Prototypen nach dem vorgeschlagenen Modell zu entwickeln. Die Arbeit gibt weiters einen Überblick über alternative Ansätze für PDMSs in der Literatur, enthält eine detaillierte Beschreibung des Modells von De Giacomo et al. und beschreibt Ergebnisse des implementierten Prototypen.Peer Data Management Systems (PDMSs) are an approach to combine the flexibility of Peer-to-Peer (P2P) systems with the expressiveness and rich semantics of database systems. In PDMSs, data is assumed to be distributed over several autonomous peers, each of them offering (parts of) their data through its own peer schema. Similar to Data Exchange and Data Integration, every peer may define mappings between the schemas of other peers and its own schema.In contrast to Data Exchange, Data Integration or Federated Databases, however, PDMSs require no global schema and therefore no global coordination to share data. Instead, all relationships are defined only between pairs of peers.Unfortunately, when applying the usual semantics based on first-order logic to these mappings, several important reasoning tasks, for example query answering, become undecidable over PDMSs for general settings.Therefore, several proposals have been presented in the literature how PDMSs could be restricted to maintain decidability for typical reasoning tasks in database theory. One possibility is to restrict the topology of the network implied by the mappings and to avoid certain kinds of cycles in the mappings. But this contradicts the idea that no global coordination is required in PDMSs.Another possibility is to restrict the expressive power of the mappings, as suggested by Calvanese et alii. Based on this idea, in 2007, De Giacomo et al. proposed a theoretical framework that allows both an arbitrary topology of the P2P network and efficient evaluation of the main reasoning tasks in Peer Data Management (PDM).Moreover it incorporates "classical" Data Exchange and Data Integration as special cases. To the best of our knowledge, this idea has not been implemented yet.Since it seems to be a promising basis for further research, the main goal of this thesis was to study the theoretical background of PDM and to create a prototype implementation of this framework. This thesis also gives an overview over the approaches for PDMSs proposed in the literature, presents the approach of De Giacomo et al. in detail and reports on the implementation and first evaluation results of the prototype.14

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

Characterizing Tractability of Simple Well-Designed Pattern Trees with Projection

International audienceAbstract We study the complexity of evaluating well-designed pattern trees, a query language extending conjunctive queries with the possibility to define parts of the query to be optional. This possibility of optional parts is important for obtaining meaningful results over incomplete data sources as it is common in semantic web settings. Recently, a structural characterization of the classes of well-designed pattern trees that can be evaluated in polynomial time was shown. However, projection—a central feature of many query languages—was not considered in this study. We work towards closing this gap by giving a characterization of all tractable classes of simple well-designed pattern trees with projection (under some common complexity theoretic assumptions). Since well-designed pattern trees correspond to the fragment of well-designed {, }-SPARQL queries this gives a complete description of the tractable classes of queries with projections in this fragment that can be characterized by the underlying graph structures of the queries. For non-simple pattern trees the tractability criteria for simple pattern trees do not capture all tractable classes. We thus extend the characterization for the non-simple case in order to capture some additional tractable cases