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Register a new userConjunctive Query Containment and Answering under Description Logics Constraints
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Diego Calvanese
Publication date
2005
fields
Informatics Engineering
and research's language is
English
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Query containment and query answering are two important computational tasks in databases. While query answering amounts to compute the result of a query over a database, query containment is the problem of checking whether for every database, the result of one query is a subset of the result of another query. In this paper, we deal with unions of conjunctive queries, and we address query containment and query answering under Description Logic constraints. Every such constraint is essentially an inclusion dependencies between concepts and relations, and their expressive power is due to the possibility of using complex expressions, e.g., intersection and difference of relations, special forms of quantification, regular expressions over binary relations, in the specification of the dependencies. These types of constraints capture a great variety of data models, including the relational, the entity-relationship, and the object-oriented model, all extended with various forms of constraints, and also the basic features of the ontology languages used in the context of the Semantic Web. We present the following results on both query containment and query answering. We provide a method for query containment under Description Logic constraints, thus showing that the problem is decidable, and analyze its computational complexity. We prove that query containment is undecidable in the case where we allow inequalities in the right-hand side query, even for very simple constraints and queries. We show that query answering under Description Logic constraints can be reduced to query containment, and illustrate how such a reduction provides upper bound results with respect to both combined and data complexity.
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We consider the task of enumerating and counting answers to $k$-ary conjunctive queries against relational databases that may be updated by inserting or deleting tuples. We exhibit a new notion of q-hierarchical conjunctive queries and show that these can be maintained efficiently in the following sense. During a linear time preprocessing phase, we can build a data structure that enables constant delay enumeration of the query results; and when the database is updated, we can update the data structure and restart the enumeration phase within constant time. For the special case of self-join free conjunctive queries we obtain a dichotomy: if a query is not q-hierarchical, then query enumeration with sublinear$^ast$ delay and sublinear update time (and arbitrary preprocessing time) is impossible. For answering Boolean conjunctive queries and for the more general problem of counting the number of solutions of k-ary queries we obtain complete dichotomies: if the querys homomorphic core is q-hierarchical, then size of the the query result can be computed in linear time and maintained with constant update time. Otherwise, the size of the query result cannot be maintained with sublinear update time. All our lower bounds rely on the OMv-conjecture, a conjecture on the hardness of online matrix-vector multiplication that has recently emerged in the field of fine-grained complexity to characterise the hardness of dynamic problems. The lower bound for the counting problem additionally relies on the orthogonal vectors conjecture, which in turn is implied by the strong exponential time hypothesis. $^ast)$ By sublinear we mean $O(n^{1-varepsilon})$ for some $varepsilon>0$, where $n$ is the size of the active domain of the current database.
We study FO-rewritability of conjunctive queries in the presence of ontologies formulated in a description logic between EL and Horn-SHIF, along with related query containment problems. Apart from providing characterizations, we establish complexity results ranging from ExpTime via NExpTime to 2ExpTime, pointing out several interesting effects. In particular, FO-rewriting is more complex for conjunctive queries than for atomic queries when inverse roles are present, but not otherwise.
We study query containment in three closely related formalisms: monadic disjunctive Datalog (MDDLog), MMSNP (a logical generalization of constraint satisfaction problems), and ontology-mediated queries (OMQs) based on expressive description logics and unions of conjunctive queries. Containment in MMSNP was known to be decidable due to a result by Feder and Vardi, but its exact complexity has remained open. We prove 2NEXPTIME-completeness and extend this result to monadic disjunctive Datalog and to OMQs.
Single-round multiway join algorithms first reshuffle data over many servers and then evaluate the query at hand in a parallel and communication-free way. A key question is whether a given distribution policy for the reshuffle is adequate for computing a given query, also referred to as parallel-correctness. This paper extends the study of the complexity of parallel-correctness and its constituents, parallel-soundness and parallel-completeness, to unions of conjunctive queries with and without negation. As a by-product it is shown that the containment problem for conjunctive queries with negation is coNEXPTIME-complete.
We investigate the computational complexity of minimizing the source side-effect in order to remove a given number of tuples from the output of a conjunctive query. In particular, given a multi-relational database $D$, a conjunctive query $Q$, and a positive integer $k$ as input, the goal is to find a minimum subset of input tuples to remove from D that would eliminate at least $k$ output tuples from $Q(D)$. This problem generalizes the well-studied deletion propagation problem in databases. In addition, it encapsulates the notion of intervention for aggregate queries used in data analysis with applications to explaining interesting observations on the output. We show a dichotomy in the complexity of this problem for the class of full conjunctive queries without self-joins by giving a characterization on the structure of $Q$ that makes the problem either polynomial-time solvable or NP-hard. Our proof of this dichotomy result already gives an exact algorithm in the easy cases; we complement this by giving an approximation algorithm for the hard cases of the problem.
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