Numerous fundamental database and reasoning problems are known to be NP-hard in general but tractable on instances where the underlying hypergraph structure is $β$-acyclic. Despite the importance of many of these problems, there has been little success in generalizing these results beyond acyclicity.
In this paper, we take on this challenge and propose nest-set width, a novel generalization of hypergraph $β$-acyclicity. We demonstrate that nest-set width has desirable properties and algorithmic significance. In particular, evaluation of boolean conjunctive queries with negation is tractable for classes with bounded nest-set width. Furthermore, propositional satisfiability is fixed-parameter tractable when parameterized by nest-set width.
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 negat…
Intersection joins over interval data are relevant in spatial and temporal data settings. A set of intervals join if their intersection is non-empty. In case of point intervals, the intersection join becomes the standard equality join. We establish the complexity of Boolean conjunctive queries with intersection joins by a many-one equivalence to disjunctions of Boolean conjunctive queries with equality joins. The complexity of any query with intersection joins is that of the hardest query with equality joins in the disjunction exhibited by our equivalence. This is captured by a new width measu…
The Shapley value is a conventional and well-studied function for determining the contribution of a player to the coalition in a cooperative game. Among its applications in a plethora of domains, it has recently been proposed to use the Shapley value for quantifying the contribution of a tuple to the result of a database query. In particular, we have a thorough understanding of the tractability frontier for the class of Conjunctive Queries (CQs) and aggregate functions over CQs. It has also been established that a tractable (randomized) multiplicative approximation exists for every union of CQ…
A well-established and fundamental insight in database theory is that negation (also known as complementation) tends to make queries difficult to process and difficult to reason about. Many basic problems are decidable and admit practical algorithms in the case of unions of conjunctive queries, but become difficult or even undecidable when queries are allowed to contain negation. Inspired by recent results in finite model theory, we consider a restricted form of negation, guarded negation. We introduce a fragment of SQL, called GN-SQL, as well as a fragment of Datalog with stratified negation,…
We propose an algorithm for answering conjunctive queries with negation, where the negated relations have bounded degree. Its data complexity matches that of the best known algorithms for the positive subquery of the input query and is expressed in terms of the fractional hypertree width and the submodular width. The query complexity depends on the structure of the negated subquery; in general it is exponential in the number of join variables occurring in negated relations yet it becomes polynomial for several classes of queries. This algorithm relies on several contributions. We show how to r…
The article investigates classes of queries maintainable by conjunctive queries (CQs) and their extensions and restrictions in the dynamic complexity framework of Patnaik and Immerman. Starting from the basic language of quantifier-free conjunctions of positive atoms, it studies the impact of additional operators and features - such as union, atomic negation and quantification - on the dynamic expressiveness, for the standard semantics as well as for Delta-semantics. Although many different combinations of these features are possible, they basically yield five important fragments for the stand…
Ontology-based query answering with existential rules is well understood and implemented for positive queries, in particular conjunctive queries. The situation changes drastically for queries with negation, where there is no agreed-upon semantics or standard implementation. Stratification, as used for Datalog, is not enough for existential rules, since the latter still admit multiple universal models that can differ on negative queries. We therefore propose universal core models as a basis for a meaningful (non-monotonic) semantics for queries with negation. Since cores are hard to compute, we…
Modern application domains such as Composite Event Recognition (CER) and real-time Analytics require the ability to dynamically refresh query results under high update rates. Traditional approaches to this problem are based either on the materialization of subresults (to avoid their recomputation) or on the recomputation of subresults (to avoid the space overhead of materialization). Both techniques have recently been shown suboptimal: instead of materializing results and subresults, one can maintain a data structure that supports efficient maintenance under updates and can quickly enumerate t…
Answering conjunctive queries (CQs) over a set of facts extended with existential rules is a prominent problem in knowledge representation and databases. This problem can be solved using the chase algorithm, which extends the given set of facts with fresh facts in order to satisfy the rules. If the chase terminates, then CQs can be evaluated directly in the resulting set of facts. The chase, however, does not terminate necessarily, and checking whether the chase terminates on a given set of rules and facts is undecidable. Numerous acyclicity notions were proposed as sufficient conditions for c…
We investigate parameterizations of both database instances and queries that make query evaluation fixed-parameter tractable in combined complexity. We introduce a new Datalog fragment with stratified negation, intensional-clique-guarded Datalog (ICG-Datalog), with linear-time evaluation on structures of bounded treewidth for programs of bounded rule size. Such programs capture in particular conjunctive queries with simplicial decompositions of bounded width, guarded negation fragment queries of bounded CQ-rank, or two-way regular path queries. Our result proceeds via compilation to alternatin…
We investigate parameterizations of both database instances and queries that make query evaluation fixed-parameter tractable in combined complexity. We show that clique-frontier-guarded Datalog with stratified negation (CFG-Datalog) enjoys bilinear-time evaluation on structures of bounded treewidth for programs of bounded rule size. Such programs capture in particular conjunctive queries with simplicial decompositions of bounded width, guarded negation fragment queries of bounded CQ-rank, or two-way regular path queries. Our result is shown by translating to alternating two-way automata, whose…
We consider the problem of exact probabilistic inference for Union of Conjunctive Queries (UCQs) on tuple-independent databases. For this problem, two approaches currently coexist. In the extensional method, query evaluation is performed by exploiting the structure of the query, and relies heavily on the use of the inclusion-exclusion principle. In the intensional method, one first builds a representation of the lineage of the query in a tractable formalism of knowledge compilation. The chosen formalism should then ensure that the probability can be efficiently computed using simple disjointne…
