539 research outputs found
Evaluating Datalog via Tree Automata and Cycluits
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 semantics is
defined via cyclic provenance circuits (cycluits) that can be tractably
evaluated.Comment: 56 pages, 63 references. Journal version of "Combined Tractability of
Query Evaluation via Tree Automata and Cycluits (Extended Version)" at
arXiv:1612.04203. Up to the stylesheet, page/environment numbering, and
possible minor publisher-induced changes, this is the exact content of the
journal paper that will appear in Theory of Computing Systems. Update wrt
version 1: latest reviewer feedbac
Query Containment for Highly Expressive Datalog Fragments
The containment problem of Datalog queries is well known to be undecidable.
There are, however, several Datalog fragments for which containment is known to
be decidable, most notably monadic Datalog and several "regular" query
languages on graphs. Monadically Defined Queries (MQs) have been introduced
recently as a joint generalization of these query languages. In this paper, we
study a wide range of Datalog fragments with decidable query containment and
determine exact complexity results for this problem. We generalize MQs to
(Frontier-)Guarded Queries (GQs), and show that the containment problem is
3ExpTime-complete in either case, even if we allow arbitrary Datalog in the
sub-query. If we focus on graph query languages, i.e., fragments of linear
Datalog, then this complexity is reduced to 2ExpSpace. We also consider nested
queries, which gain further expressivity by using predicates that are defined
by inner queries. We show that nesting leads to an exponentially increasing
hierarchy for the complexity of query containment, both in the linear and in
the general case. Our results settle open problems for (nested) MQs, and they
paint a comprehensive picture of the state of the art in Datalog query
containment.Comment: 20 page
The Dichotomy of Evaluating Homomorphism-Closed Queries on Probabilistic Graphs
We study the problem of probabilistic query evaluation on probabilistic
graphs, namely, tuple-independent probabilistic databases on signatures of
arity two. Our focus is the class of queries that is closed under
homomorphisms, or equivalently, the infinite unions of conjunctive queries. Our
main result states that all unbounded queries from this class are #P-hard for
probabilistic query evaluation. As bounded queries from this class are
equivalent to a union of conjunctive queries, they are already classified by
the dichotomy of Dalvi and Suciu (2012). Hence, our result and theirs imply a
complete data complexity dichotomy, between polynomial time and #P-hardness,
for evaluating infinite unions of conjunctive queries over probabilistic
graphs. This dichotomy covers in particular all fragments of infinite unions of
conjunctive queries such as negation-free (disjunctive) Datalog, regular path
queries, and a large class of ontology-mediated queries on arity-two
signatures. Our result is shown by reducing from counting the valuations of
positive partitioned 2-DNF formulae for some queries, or from the
source-to-target reliability problem in an undirected graph for other queries,
depending on properties of minimal models. The presented dichotomy result
applies to even a special case of probabilistic query evaluation called
generalized model counting, where fact probabilities must be 0, 0.5, or 1.Comment: 30 pages. Journal version of the ICDT'20 paper
https://drops.dagstuhl.de/opus/volltexte/2020/11939/. Submitted to LMCS. The
previous version (version 2) was the same as the ICDT'20 paper with some
minor formatting tweaks and 7 extra pages of technical appendi
gMark: Schema-Driven Generation of Graphs and Queries
Massive graph data sets are pervasive in contemporary application domains.
Hence, graph database systems are becoming increasingly important. In the
experimental study of these systems, it is vital that the research community
has shared solutions for the generation of database instances and query
workloads having predictable and controllable properties. In this paper, we
present the design and engineering principles of gMark, a domain- and query
language-independent graph instance and query workload generator. A core
contribution of gMark is its ability to target and control the diversity of
properties of both the generated instances and the generated workloads coupled
to these instances. Further novelties include support for regular path queries,
a fundamental graph query paradigm, and schema-driven selectivity estimation of
queries, a key feature in controlling workload chokepoints. We illustrate the
flexibility and practical usability of gMark by showcasing the framework's
capabilities in generating high quality graphs and workloads, and its ability
to encode user-defined schemas across a variety of application domains.Comment: Accepted in November 2016. URL:
http://ieeexplore.ieee.org/document/7762945/. in IEEE Transactions on
Knowledge and Data Engineering 201
Towards Efficient Reasoning under Guarded-based Disjunctive Existential Rules
International audienceThe complete picture of the complexity of answering (unions of) conjunctive queries under the main guarded-based classes of disjunc- tive existential rules has been recently settled. It has been shown that the problem is very hard, namely 2ExpTime-complete, even for fixed sets of rules expressed in lightweight formalisms. This gives rise to the question whether its complexity can be reduced by restricting the query language. Several subclasses of conjunctive queries have been proposed with the aim of reducing the complexity of classical database problems such as query evaluation and query containment. Three of the most prominent subclasses of this kind are queries of bounded hypertree-width, queries of bounded treewidth and acyclic queries. The central objective of the present paper is to understand whether the above query languages have a positive impact on the complexity of query answering under the main guarded-based classes of disjunctive existential rules. We show that (unions of) conjunctive queries of bounded hypertree- width and of bounded treewidth do not reduce the complexity of our problem, even if we focus on predicates of bounded arity, or on fixed sets of disjunctive existential rules. Regarding acyclic queries, although our problem remains 2ExpTime-complete in general, in some relevant set- tings the complexity reduces to ExpTime-complete; in fact, this requires to bound the arity of the predicates, and for some expressive guarded- based formalisms, to fix the set of rules
Characterising Fixed Parameter Tractability for Query Evaluation over Guarded TGDs
We consider the parameterized complexity of evaluating Ontology Mediated Queries (OMQ) based on Guarded TGDs (GTGD) and Unions of Conjunctive Queries, in the case where relational symbols have unrestricted arity and where the parameter is the size of the OMQ. We establish exact criteria for fixed-parameter tractable (fpt) evaluation of recursively enumerable (r.e.) classes of such OMQs (under the widely held Exponential Time Hypothesis). One of the main technical tools introduced in the paper is an fpt-reduction from deciding parameterized uniform CSPs to parameterized OMQ evaluation. The reduction preserves measures known to be essential for classifying r.e. classes of parameterized uniform CSPs: submodular width (according to the well known result of Marx for unrestricted-arity schemas) and treewidth (according to the well known result of Grohe for bounded-arity schemas). As such, it can be employed to obtain hardness results for evaluation of r.e. classes of parameterized OMQs based on GTGD both in the unrestricted and in the bounded arity case. Previously, for bounded arity schemas, this has been tackled using a technique requiring full introspection into the construction employed by Grohe
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
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