When finding exact answers to a query over a large database is infeasible, it is natural to approximate the query by a more efficient one that comes from a class with good bounds on the complexity of query evaluation. In this paper we study such approximations for conjunctive queries. These queries are of special importance in databases, and we have a very good understanding of the classes that admit fast query evaluation, such as acyclic, or bounded (hyper)treewidth queries.We define approximations of a given query Q as queries from one of those classes that disagree with Q as little as possible. We mostly concentrate on approximations that are guaranteed to return correct answers. We prove that for the above classes of tractable conjunctive queries, approximations always exist, and are at most polynomial in the size of the original query. This follows from general results we establish that relate closure properties of classes of conjunctive queries to the existence of approximations. We also show that in many cases, the size of approximations is bounded by the size of the query they approximate. We establish a number of results showing how combinatorial properties of queries affect properties of their approximations, study bounds on the number of approximations, as well as the complexity of finding and identifying approximations. We also look at approximations that return all correct answers and study their properties.
The original SPARQL proposal was often criticized for its inability to navigate through the structure of RDF documents. For this reason property paths were introduced in SPARQL 1.1, but up to date there are no theoretical studies examining how their addition to the language affects main computational tasks such as query evaluation, query containment, and query subsumption. In this paper we tackle all of these problems and show that although the addition of property paths has no impact on query evaluation, they do make the containment and subsumption problems substantially more difficult.
Graph databases are currently one of the most popular paradigms for storing data. One of the key conceptual differences between graph and relational databases is the focus on navigational queries that ask whether some nodes are connected by paths satisfying certain restrictions. This focus has driven the definition of several different query languages and the subsequent study of their fundamental properties.We define the graph query language of Regular Queries, which is a natural extension of unions of conjunctive 2-way regular path queries (UC2RPQs) and unions of conjunctive nested 2-way regular path queries (UCN2RPQs). Regular queries allow expressing complex regular patterns between nodes. We formalize regular queries as nonrecursive Datalog programs with transitive closure rules. This language has been previously considered, but its algorithmic properties are not well understood.Our main contribution is to show elementary tight bounds for the containment problem for regular queries. Specifically, we show that this problem is 2Expspace-complete. For all extensions of regular queries known to date, the containment problem turns out to be nonelementary. Together with the fact that evaluating regular queries is not harder than evaluating UCN2RPQs, our results show that regular queries achieve a good balance between expressiveness and complexity, and constitute a well-behaved class that deserves further investigation.
It is known that unions of acyclic conjunctive queries (CQs) can be evaluated in linear time, as opposed to arbitrary CQs, for which the evaluation problem is NP-complete. It follows from techniques in the area of constraint-satisfaction problems that semantically acyclic unions of CQs -i.e., unions of CQs that are equivalent to a union of acyclic ones -can be evaluated in polynomial time, though testing membership in the class of semantically acyclic CQs is NP-complete.We study here the fundamental notion of semantic acyclicity in the context of graph databases and unions of conjunctive regular path queries with inverse (UC2RPQs). It is known that unions of acyclic C2RPQs can be evaluated efficiently, but it is by no means obvious whether the same holds for the class of UC2RPQs that are semantically acyclic. We prove that checking whether a UC2RPQ is semantically acyclic is decidable in 2Expspace, and that it is Expspacehard even in the absence of inverses. Furthermore, we show that evaluation of semantically acyclic UC2RPQs is fixedparameter tractable. In addition, our tools yield a strong theory of approximations for UC2RPQs when no equivalent acyclic UC2RPQ exists.
When finding exact answers to a query over a large database is infeasible, it is natural to approximate the query by a more efficient one that comes from a class with good bounds on the complexity of query evaluation. In this paper we study such approximations for conjunctive queries. These queries are of special importance in databases, and we have a very good understanding of the classes that admit fast query evaluation, such as acyclic, or bounded (hyper)treewidth queries.We define approximations of a given query Q as queries from one of those classes that disagree with Q as little as possible. We mostly concentrate on approximations that are guaranteed to return correct answers. We prove that for the above classes of tractable conjunctive queries, approximations always exist, and are at most polynomial in the size of the original query. This follows from general results we establish that relate closure properties of classes of conjunctive queries to the existence of approximations. We also show that in many cases, the size of approximations is bounded by the size of the query they approximate. We establish a number of results showing how combinatorial properties of queries affect properties of their approximations, study bounds on the number of approximations, as well as the complexity of finding and identifying approximations. We also look at approximations that return all correct answers and study their properties.
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