A Dichotomy for Homomorphism Closed Queries on Probalistic Graphs

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A Dichotomy for Homomorphism Closed Queries on Probalistic Graphs
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CC Attribution 3.0 Germany:
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2020
Language
English

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Abstract
We study the problem of probabilistic query evaluation (PQE) over probabilistic graphs, namely, tuple-independent probabilistic databases (TIDs) 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, denoted UCQ∞. Our main result states that all unbounded queries in UCQ∞ are #P-hard for PQE. As bounded queries in UCQ∞ are already classified by the dichotomy of Dalvi and Suciu [Dalvi and Suciu, 2012], our results and theirs imply a complete dichotomy on PQE for UCQ∞ queries over probabilistic graphs. This dichotomy covers in particular all fragments in UCQ∞ 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 (#PP2DNF) for some queries, or from the source-to-target reliability problem in an undirected graph (#U-ST-CON) for other queries, depending on properties of minimal models.
NP-hard Pulse (signal processing) Suite (music) Morphing Spezielle orthogonale Gruppe State of matter Differential (mechanical device) Plotter Multiplication sign Range (statistics) Back-face culling Fault-tolerant system Mereology Repeating decimal Junction (traffic) Subset Usability Formal language Software bug Impulse response Matrix (mathematics) Core dump Kerr-Lösung Data conversion Area Intelligent Network Boss Corporation Simulation Theory of relativity Rational number Maxima and minima Knot Instance (computer science) Oscillation Demoscene Degree (graph theory) Type theory Proof theory Arithmetic mean Exploratory data analysis Mathematical singularity XING MiniDisc Website Summierbarkeit Moving average Right angle Pattern language Quicksort Writing Resultant Thomas Bayes Sine Observational study Information systems Mögliche-Welten-Semantik Control flow Random matrix Dichotomy Rule of inference Computer Number Bargaining problem Latent heat Goodness of fit Pi Causality IRIS-T Green's function Reduction of order OSI model Data structure Booting Airfoil Distribution (mathematics) Graph (mathematics) Matching (graph theory) Key (cryptography) Quantum state Artificial neural network Bit error rate Forcing (mathematics) Horizon Database Grass (card game) 8 (number) Word Logic Personal digital assistant Network topology Universe (mathematics) Iteration
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