Abstract not found

SPARQL is the standard language for querying RDF data. In this article, we address systematically the formal study of the database aspects of SPARQL, concentrating in its graph pattern matching facility. We provide a compositional semantics for the core part of SPARQL, and study the complexity of the evaluation of several fragments of the language. Among other complexity results, we show that the evaluation of general SPARQL patterns is PSPACE-complete. We identify a large class of SPARQL patterns, defined by imposing a simple and natural syntactic restriction, where the query evaluation problem can be solved more efficiently. This restriction gives rise to the class of well-designed patterns. We show that the evaluation problem is coNP-complete for well-designed patterns. Moreover, we provide several rewriting rules for well-designed patterns whose application may have a considerable impact in the cost of evaluating SPARQL queries.

We compare tractable classes of constraint satisfaction problems (CSPs). We first give a uniform presentation of the major structural CSP decomposition methods. We then introduce a new class of tractable CSPs based on the concept of hypertree decomposition recently developed in Database Theory. We introduce a framework for comparing parametric decomposition-based methods according to tractability criteria and compare the most relevant methods. We show that the method of hypertree decomposition dominates the others in the case of general (nonbinary) CSPs.

Several important decision problems on conjunctive queries (CQs) are NP-complete in general but become tractable, and actually highly parallelizable, if restricted to acyclic or nearly acyclic queries. Examples are the evaluation of Boolean CQs and query containment. These problems were shown tractable for conjunctive queries of bounded treewidth [7], and of bounded degree of cyclicity [18, 17]. The so far most general concept of nearly acyclic queries was the notion of queries of bounded query-width introduced by Chekuri and Rajaraman [7]. While CQs of bounded query width are tractable, it remained unclear whether such queries are efficiently recognizable. Chekuri and Rajaraman [7] stated as an open problem whether for each constant k it can be determined in polynomial time if a query has query width ≤ k. We give a negative answer by proving this problem NP-complete (specifically, for k = 4). In order to circumvent this difficulty, we introduce the new concept of hypertree decomposition of a query and the corresponding notion of hypertree width. We prove: (a) for each k, the class of queries with query width bounded by k is properly contained in the class of queries whose hypertree width is bounded by k; (b) unlike query width, constant hypertree-width is efficiently recognizable; (c) Boolean queries of constant hypertree width can be efficiently evaluated.

The paper considers two decision problems on hypergraphs, hypergraph saturation and recognition of the transversal hypergraph, and discusses their significance for several search problems in applied computer science. Hypergraph saturation, i.e., given a hypergraph H, decide if every subset of vertices is contained in or contains some edge of H, is shown to be co-NP-complete. A certain subproblem of hypergraph saturation, the saturation of simple hypergraphs, is shown to be computationally equivalent to transversal hypergraph recognition, i.e., given two hypergraphs H 1; H 2, decide if the sets in H 2 are all the minimal transversals of H 1. The complexity of the search problem related to the recognition of the transversal hypergraph, the computation of the transversal hypergraph, is an open problem. This task needs time exponential in the input size, but it is unknown whether an output-polynomial algorithm exists for this problem. For several important subcases, for instance if an upper or lower bound is imposed on the edge size or for acyclic hypergraphs, we present output-polynomial algorithms. Computing or recognizing the minimal transversals of a hypergraph is a frequent problem in practice, which is pointed out by identifying important applications in database theory, Boolean switching theory, logic, and AI, particularly in model-based diagnosis.

We present an approach to the solution of decision problems formulated as influence diagrams. This approach involves a special triangulation of the underlying graph, the construction of a junction tree with special properties, and a message passing algorithm operating on the junction tree for computation of expected utilities and optimal decision policies.

The chase algorithm is a fundamental tool for query evaluation and for testing query containment under tuple-generating dependencies (TGDs) and equality-generating dependencies (EGDs). So far, most of the research on this topic has focused on cases where the chase procedure terminates. This paper introduces expressive classes of TGDs defined via syntactic restrictions: guarded TGDs (GTGDs) and weakly guarded sets of TGDs (WGT-GDs). For these classes, the chase procedure is not guaranteed to terminate and thus may have an infinite outcome. Nevertheless, we prove that the problems of conjunctive-query answering and query containment under such TGDs are decidable. We provide decision procedures and tight complexity bounds for these problems. Then we show how EGDs can be incorporated into our results by providing conditions under which EGDs do not harmfully interact with TGDs and do not affect the decidability and complexity of query answering. We show applications of the aforesaid classes of constraints to the problem of answering conjunctive queries in F-Logic Lite, an object-oriented ontology language, and in some tractable Description Logics. 1.

Abstract. Database schemes (winch, intuitively, are collecuons of table skeletons) can be wewed as hypergraphs (A hypergraph Is a generalization of an ordinary undirected graph, such that an edge need not contain exactly two nodes, but can instead contain an arbitrary nonzero number of nodes.) A class of "acychc " database schemes was recently introduced. A number of basic desirable propemes of database schemes have been shown to be equivalent to acyclicity This shows the naturalness of the concept. However, unlike the situation for ordinary, undirected graphs, there are several natural, noneqmvalent notions of acyclicity for hypergraphs (and hence for database schemes). Various desirable properties of database schemes are constdered and it is shown that they fall into several equivalence classes, each completely characterized by the degree of acycliclty of the scheme The results are also of interest from a purely graph-theoretic viewpomt. The original notion of aeyclicity has the countermtmtive property that a subhypergraph of an acychc hypergraph can be cyclic. This strange behavior does not occur for the new degrees of acyelicity that are considered.

This paper deals with the evaluation of acyclic Boolean conjunctive queries in relational databases. By well-known results of Yannakakis [1981], this problem is solvable in polynomial time; its precise complexity, however, has not been pinpointed so far. We show that the problem of evaluating acyclic Boolean conjunctive queries is complete for LOGCFL, the class of decision problems that are logspace-reducible to a context-free language. Since LOGCFL is contained in AC 1 and NC 2, the evaluation problem of acyclic Boolean conjunctive queries is highly parallelizable. We present a parallel database algorithm solving this problem with a logarithmic number of parallel join operations. The algorithm is generalized to computing the output of relevant classes of non-Boolean queries. We also show that the acyclic versions of the following well-known database and AI problems are all LOGCFL-complete: The Query Output Tuple problem for conjunctive queries, Conjunctive Query Containment, Clause Subsumption, and Constraint Satisfaction. The LOGCFL-completeness result is extended to the class of queries of bounded treewidth and to other relevant query classes which are more general than the acyclic queries.

There is a very close relationship between constraint satisfaction problems and the satisfaction of join-dependencies in a relational database which is due to a common underlying structure, namely a hypergraph. By making that relationship explicit we are able to adapt techniques previously developed for the study of relational databases to obtain new results for constraint satisfaction problems. In particular, we prove that a constraint satisfaction problem may be decomposed into a number of subproblems precisely when the corresponding hypergraph satisfies a simple condition. We show that combining this decomposition approach with existing algorithms can lead to a significant improvement in efficiency.