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^\infty. Our main result states that all unbounded queries in UCQ^\infty are #P-hard for PQE. As bounded queries in UCQ^\infty are already classified by the dichotomy of Dalvi and Suciu [17], our results and theirs imply a complete dichotomy on PQE for UCQ^\infty queries over probabilistic graphs. This dichotomy covers in particular all fragments in UCQ^\infty 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.

中文翻译：

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概率图上同态封闭查询的二分法

我们研究概率图上的概率查询评估 (PQE) 问题，即元组二签名上的元组独立概率数据库 (TID)。我们的重点是在同态下封闭的查询类，或者等价地，连接查询的无限并集，表示为 UCQ^\infty。我们的主要结果表明，UCQ^\infty 中的所有无界查询对于 PQE 都是 #P-hard。由于 UCQ^\infty 中的有界查询已经按照 Dalvi 和 Suciu [17] 的二分法进行了分类，我们的结果和他们的结果暗示了对概率图上的 UCQ^\infty 查询的 PQE 的完整二分法。这种二分法特别涵盖了 UCQ^\infty 中的所有片段，例如无否定（析取）数据日志、常规路径查询和一大类对二元签名的本体中介查询。