The Dichotomy of Evaluating Homomorphism-Closed Queries on Probabilistic Graphs

We study the problem of query evaluation on probabilistic graphs, namely, tuple-independent probabilistic databases over signatures of arity two. We focus on the class of queries closed under homomorphisms, or, equivalently, the infinite unions of conjunctive queries. Our main result states that the probabilistic query evaluation problem is #P-hard for all unbounded queries from this class. 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, on evaluating homomorphism-closed queries over probabilistic graphs. This dichotomy covers in particular all fragments of infinite unions of conjunctive queries over arity-two signatures, such as negation-free (disjunctive) Datalog, regular path queries, and a large class of ontology-mediated queries. The dichotomy also applies to a restricted case of probabilistic query evaluation called generalized model counting, where fact probabilities must be 0, 0.5, or 1. We show the main result by reducing from the problem of counting the valuations of positive partitioned 2-DNF formulae, or from the source-to-target reliability problem in an undirected graph, depending on properties of minimal models for the query.

Efficiently Estimating Joining Cost of Subqueries in Regular Path Queries

Evaluating Regular Path Queries (RPQs) have been of interest since they were used as a powerful way to explore paths and patterns in graph databases. Traditional automata-based approaches are restricted in the graph size and/or highly complex queries, which causes a high evaluation cost (e.g., memory space and response time) on large graphs. Recently, although using the approach based on the threshold rare label for large graphs has been achieving some success, they could not often guarantee the minimum searching cost. Alternatively, the Unit-Subquery Cost Matrix (USCM) has been studied and obtained the viability of the usage of subqueries. Nevertheless, this method has an issue, which is, it does not cumulate the cost among subqueries that causes the long response time on a large graph. In order to overcome this issue, this paper proposes a method for estimating joining cost of subqueries to accelerate the USCM based parallel evaluation of RPQs on a large graph, namely USCM-Join. Through real-world datasets, we experimentally show that the USCM-Join outperforms others and estimating the joining cost enhances the USCM based approach up to around 20% in terms of response time.

Finite Controllability for Ontology-Mediated Query Answering of CRPQ

Finite ontology mediated query answering (FOMQA) is the variant of ontology mediated query answering (OMQA) where the represented world is assumed to be finite, and thus only finite models of the ontology are considered. We study the property of finite-controllability, that is, whether FOMQA and OMQA are equivalent, for fragments of C2RPQ. C2RPQ is the language of conjunctive two-way regular path queries, which can be regarded as the result of adding simple recursion to Conjunctive Queries. For graph classes S, we consider fragments C2RPQ(S) of C2RPQ as the queries whose underlying graph structure is in S. We completely classify the finitely controllable and non-finitely controllable fragments under: inclusion dependencies, (frontier-)guarded rules, frontier-one rules (either with or without constants), and more generally under guarded-negation first-order constraints. For the finitely controllable fragments, we show a reduction to the satisfiability problem for guarded-negation first-order logic, yielding a 2EXPTIME algorithm (in combined complexity) for the corresponding (F)OMQA problem.

Containment of Simple Conjunctive Regular Path Queries

Testing containment of queries is a fundamental reasoning task in knowledge representation. We study here the containment problem for Conjunctive Regular Path Queries (CRPQs), a navigational query language extensively used in ontology and graph database querying. While it is known that containment of CRPQs is EXPSPACE-complete in general, we focus here on severely restricted fragments, which are known to be highly relevant in practice according to several recent studies. We obtain a detailed overview of the complexity of the containment problem, depending on the features used in the regular expressions of the queries, with completeness results for NP, Pi2p, PSPACE or EXPSPACE.