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A paramount challenge in probabilistic databases is the scalable computation of confidences of tuples in query results. This paper introduces an efficient secondary-storage operator for exact computation of queries on tuple-independent probabilistic databases. We consider the conjunctive queries without self-joins that are known to be tractable on any tuple-independent database, and queries that are not tractable in general but become tractable on probabilistic databases restricted by functional dependencies. Our operator is semantically equivalent to a sequence of aggregations and can be naturally integrated into existing relational query plans. As a proof of concept, we developed an extension of the PostgreSQL 8.3.3 query engine called SPROUT. We study optimizations that push or pull our operator or parts thereof past joins. The operator employs static information, such as the query structure and functional …