A PC Chase

PC stands for path-conjunctive, the name of a class of queries and dependencies that we define over complex values with dictionaries. This class includes the relational conjunctive queries and embedded dependencies, as well as many interesting examples of complex value and oodb queries and integrity constraints. We show that some important classical results on containment, dependency implication, and chasing extend and generalize to this class

Physical Data Independence, Constraints and Optimization with Universal Plans

We present an optimization method and al gorithm designed for three objectives: physi cal data independence, semantic optimization, and generalized tableau minimization. The method relies on generalized forms of chase and backchase with constraints (dependen cies). By using dictionaries (finite functions) in physical schemas we can capture with con straints useful access structures such as indexes, materialized views, source capabilities, access support relations, gmaps, etc. The search space for query plans is defined and enumerated in a novel manner: the chase phase rewrites the original query into a universal plan that integrates all the access structures and alternative pathways that are allowed by appli cable constraints. Then, the backchase phase produces optimal plans by eliminating various combinations of redundancies, again according to constraints. This method is applicable (sound) to a large class of queries, physical access structures, and semantic constraints. We prove that it is in fact complete for path-conjunctive queries and views with complex objects, classes and dictio naries, going beyond previous theoretical work on processing queries using materialized views

Query reformulation with constraints

Let Σ1, Σ2 be two schemas, which may overlap, C be a set of constraints on the joint schema Σ1 ∪ Σ2, and q1 be a Σ1-query. An (equivalent) reformulation of q1 in the presence of C is a Σ2-query, q2, such that q2 gives the same answers as q1 on any Σ1 ∪ Σ2-database instance that satisfies C. In general, there may exist multiple such reformulations and choosing among them may require, for example, a cost model

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

On Chase Termination Beyond Stratification

We study the termination problem of the chase algorithm, a central tool in various database problems such as the constraint implication problem, Conjunctive Query optimization, rewriting queries using views, data exchange, and data integration. The basic idea of the chase is, given a database instance and a set of constraints as input, to fix constraint violations in the database instance. It is well-known that, for an arbitrary set of constraints, the chase does not necessarily terminate (in general, it is even undecidable if it does or not). Addressing this issue, we review the limitations of existing sufficient termination conditions for the chase and develop new techniques that allow us to establish weaker sufficient conditions. In particular, we introduce two novel termination conditions called safety and inductive restriction, and use them to define the so-called T-hierarchy of termination conditions. We then study the interrelations of our termination conditions with previous conditions and the complexity of checking our conditions. This analysis leads to an algorithm that checks membership in a level of the T-hierarchy and accounts for the complexity of termination conditions. As another contribution, we study the problem of data-dependent chase termination and present sufficient termination conditions w.r.t. fixed instances. They might guarantee termination although the chase does not terminate in the general case. As an application of our techniques beyond those already mentioned, we transfer our results into the field of query answering over knowledge bases where the chase on the underlying database may not terminate, making existing algorithms applicable to broader classes of constraints.Comment: Technical Report of VLDB 2009 conference versio

Worst-case Optimal Query Answering for Greedy Sets of Existential Rules and Their Subclasses

The need for an ontological layer on top of data, associated with advanced reasoning mechanisms able to exploit the semantics encoded in ontologies, has been acknowledged both in the database and knowledge representation communities. We focus in this paper on the ontological query answering problem, which consists of querying data while taking ontological knowledge into account. More specifically, we establish complexities of the conjunctive query entailment problem for classes of existential rules (also called tuple-generating dependencies, Datalog+/- rules, or forall-exists-rules. Our contribution is twofold. First, we introduce the class of greedy bounded-treewidth sets (gbts) of rules, which covers guarded rules, and their most well-known generalizations. We provide a generic algorithm for query entailment under gbts, which is worst-case optimal for combined complexity with or without bounded predicate arity, as well as for data complexity and query complexity. Secondly, we classify several gbts classes, whose complexity was unknown, with respect to combined complexity (with both unbounded and bounded predicate arity) and data complexity to obtain a comprehensive picture of the complexity of existential rule fragments that are based on diverse guardedness notions. Upper bounds are provided by showing that the proposed algorithm is optimal for all of them