Propagating functional dependencies with conditions

The dependency propagation problem is to determine, given a view defined on data sources and a set of dependencies on the sources, whether another dependency is guaranteed to hold on the view. This paper investigates dependency propagation for recently proposed conditional functional dependencies (CFDs). The need for this study is evident in data integration, exchange and cleaning since dependencies on data sources often only hold conditionally on the view. We investigate dependency propagation for views defined in various fragments of relational algebra, CFDs as view dependencies, and for source dependencies given as either CFDs or traditional functional dependencies (FDs). (a) We establish lower and upper bounds, all matching , ranging from PTIME to undecidable. These not only provide the first results for CFD propagation, but also extend the classical work of FD propagation by giving new complexity bounds in the presence of finite domains. (b) We provide the first algorithm for computing a minimal cover of all CFDs propagated via SPC views; the algorithm has the same complexity as one of the most efficient algorithms for computing a cover of FDs propagated via a projection view, despite the increased expressive power of CFDs and SPC views. (c) We experimentally verify that the algorithm is efficient. </jats:p

View Selection in Semantic Web Databases

We consider the setting of a Semantic Web database, containing both explicit data encoded in RDF triples, and implicit data, implied by the RDF semantics. Based on a query workload, we address the problem of selecting a set of views to be materialized in the database, minimizing a combination of query processing, view storage, and view maintenance costs. Starting from an existing relational view selection method, we devise new algorithms for recommending view sets, and show that they scale significantly beyond the existing relational ones when adapted to the RDF context. To account for implicit triples in query answers, we propose a novel RDF query reformulation algorithm and an innovative way of incorporating it into view selection in order to avoid a combinatorial explosion in the complexity of the selection process. The interest of our techniques is demonstrated through a set of experiments.Comment: VLDB201

Querying Schemas With Access Restrictions

We study verification of systems whose transitions consist of accesses to a Web-based data-source. An access is a lookup on a relation within a relational database, fixing values for a set of positions in the relation. For example, a transition can represent access to a Web form, where the user is restricted to filling in values for a particular set of fields. We look at verifying properties of a schema describing the possible accesses of such a system. We present a language where one can describe the properties of an access path, and also specify additional restrictions on accesses that are enforced by the schema. Our main property language, AccLTL, is based on a first-order extension of linear-time temporal logic, interpreting access paths as sequences of relational structures. We also present a lower-level automaton model, Aautomata, which AccLTL specifications can compile into. We show that AccLTL and A-automata can express static analysis problems related to "querying with limited access patterns" that have been studied in the database literature in the past, such as whether an access is relevant to answering a query, and whether two queries are equivalent in the accessible data they can return. We prove decidability and complexity results for several restrictions and variants of AccLTL, and explain which properties of paths can be expressed in each restriction.Comment: VLDB201

Query evaluation revised: parallel, distributed, via rewritings

This is a thesis on query evaluation in parallel and distributed settings, and structurally simple rewritings. It consists of three parts. In the first part, we investigate the efficiency of constant-time parallel evaluation algorithms. That is, the number of required processors or, asymptotically equivalent, the work required to evaluate queries in constant time. It is known that relational algebra queries can be evaluated in constant time. However, work-efficiency has not been a focus, and indeed known evaluation algorithms yield huge (polynomial) work bounds. We establish work-efficient constant-time algorithms for several query classes: (free-connex) acyclic, semi-join algebra, and natural join queries; the latter in the worst-case framework. The second part is about deciding parallel-correctness of distributed evaluation strategies: Given a query and policies specifying how data is distributed and communicated among multiple servers, does the distributed evaluation yield the same result as the classical evaluation, for every database? Ketsman et al. proved that parallel-correctness for Datalog is undecidable; by reduction from the undecidable containment problem for Datalog. We show that parallel-correctness is already undecidable for monadic and frontier-guarded Datalog queries, for which containment is decidable. However, deciding parallel-correctness for frontier-guarded Datalog and constraint-based communication policies satisfying a certain property is 2ExpTime-complete. Furthermore, we obtain the same bounds for the parallel-boundedness problem, which asks whether the number of required communication rounds is bounded, over all databases. The third part is about structurally simple rewritings. The (classical) rewriting problem asks whether, for a given query and a set of views, there is a query, called rewriting, over the views that is equivalent to the given query. We study the variant of this problem for (subclasses of) conjunctive queries and views that asks for a structurally simple rewriting. We prove that, if the given query is acyclic, an acyclic rewriting exists if there is any rewriting at all. Analogous statements hold for free-connex acyclic, hierarchical, and q-hierarchical queries. Furthermore, we prove that the problem is NP-hard, even if the given query and the views are acyclic or hierarchical. It becomes tractable if the views are free-connex acyclic or q-hierarchical (and the arity of the database schema is bounded)

Tree Projections and Constraint Optimization Problems: Fixed-Parameter Tractability and Parallel Algorithms

Tree projections provide a unifying framework to deal with most structural decomposition methods of constraint satisfaction problems (CSPs). Within this framework, a CSP instance is decomposed into a number of sub-problems, called views, whose solutions are either already available or can be computed efficiently. The goal is to arrange portions of these views in a tree-like structure, called tree projection, which determines an efficiently solvable CSP instance equivalent to the original one. Deciding whether a tree projection exists is NP-hard. Solution methods have therefore been proposed in the literature that do not require a tree projection to be given, and that either correctly decide whether the given CSP instance is satisfiable, or return that a tree projection actually does not exist. These approaches had not been generalized so far on CSP extensions for optimization problems, where the goal is to compute a solution of maximum value/minimum cost. The paper fills the gap, by exhibiting a fixed-parameter polynomial-time algorithm that either disproves the existence of tree projections or computes an optimal solution, with the parameter being the size of the expression of the objective function to be optimized over all possible solutions (and not the size of the whole constraint formula, used in related works). Tractability results are also established for the problem of returning the best K solutions. Finally, parallel algorithms for such optimization problems are proposed and analyzed. Given that the classes of acyclic hypergraphs, hypergraphs of bounded treewidth, and hypergraphs of bounded generalized hypertree width are all covered as special cases of the tree projection framework, the results in this paper directly apply to these classes. These classes are extensively considered in the CSP setting, as well as in conjunctive database query evaluation and optimization

Ronciling Differences

In this paper we study a problem motivated by the management of changes in databases. It turns out that several such change scenarios, e.g., the separately studied problems of view maintenance (propagation of data changes) and view adaptation (propagation of view definition changes) can be unified as instances of query reformulation using views provided that support for the relational difference operator exists in the context of query reformulation. Exact query reformulation using views in positive relational languages is well understood, and has a variety of applications in query optimization and data sharing. Unfortunately, most questions about queries become undecidable in the presence of difference (or negation), whether we use the foundational set semantics or the more practical bag semantics. We present a new way of managing this difficulty by defining a novel semantics, Z- relations, where tuples are annotated with positive or negative integers. Z-relations conveniently represent data, insertions, and deletions in a uniform way, and can apply deletions with the union operator (deletions are tuples with negative counts). We show that under Z-semantics relational algebra (R A) queries have a normal form consisting of a single difference of positive queries, and this leads to the decidability of their equivalence.We provide a sound and complete algorithm for reformulating R A queries, including queries with difference, over Z-relations. Additionally, we show how to support standard view maintenanc

When Can We Answer Queries Using Result-Bounded Data Interfaces?

We consider answering queries on data available through access methods, that provide lookup access to the tuples matching a given binding. Such interfaces are common on the Web; further, they often have bounds on how many results they can return, e.g., because of pagination or rate limits. We thus study result-bounded methods, which may return only a limited number of tuples. We study how to decide if a query is answerable using result-bounded methods, i.e., how to compute a plan that returns all answers to the query using the methods, assuming that the underlying data satisfies some integrity constraints. We first show how to reduce answerability to a query containment problem with constraints. Second, we show "schema simplification" theorems describing when and how result bounded services can be used. Finally, we use these theorems to give decidability and complexity results about answerability for common constraint classes.Comment: 65 pages; journal version of the PODS'18 paper arXiv:1706.0793