A Dichotomy for Homomorphism-Closed Queries on Probabilistic Graphs

Authors Antoine Amarilli , İsmail İlkan Ceylan

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Antoine Amarilli
  • LTCI, Télécom Paris, Institut Polytechnique de Paris, France
İsmail İlkan Ceylan
  • University of Oxford, United Kingdom

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Antoine Amarilli and İsmail İlkan Ceylan. A Dichotomy for Homomorphism-Closed Queries on Probabilistic Graphs. In 23rd International Conference on Database Theory (ICDT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 155, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Database query processing and optimization (theory)
  • Tuple-independent database
  • #P-hardness
  • recursive queries
  • homomorphism-closed queries


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