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.

Design and Simulation of Radial Flow Turbine Impeller and Investigation Thermodynamic Properties of Flow in LE and TE

Centrifugal (radial flow) turbines are widely used in various industries, including power generation industries, so the study on them is of particular importance. The aim of this study was to investigate the thermodynamic properties of fluid flow in Trailing Edge (TE) and (LE) Leading Edge. For this purpose, first, the rotor (impeller) of the radial flow turbine was designed based on some design data such as flow rate, number of blades, rotational speed, diameter and length of the impeller, and then the designed rotor was simulated in 3D. The simulation done in the pressure based method and the turbulence model is SST and the rotational speed was 140,000(RPM). The results showed that the pressure, temperature and enthalpy in TE are less than LE and the areas close to the hub have the highest pressure. Another phenomenon observed is that in the section LE we see the separation of the flow from the blade surface, which then approaches the blade surface again and follows a relatively regular path,so the entropy in TE is greater than LE. At the end, the results of numerical solution were compared with valid data and the error rate and its reasons were discussed.

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.