#### Abstract

This paper investigates the problem of efficiently computing the confidences of distinct tuples in the answers to conjunctive queries with inequalities (<) on tuple-independent probabilistic databases. This problem is fundamental to probabilistic databases and was recently stated open.
Our contributions are of both theoretical and practical importance. We define a class of tractable queries with inequalities, and generalize existing results on #P-hardness of query evaluation, now in the presence of inequalities.
For the tractable queries, we introduce a confidence computation technique based on efficient compilation of the lineage of the query answer into Ordered Binary Decision Diagrams (OBDDs), whose sizes are linear in the number of variables of the lineage.
We implemented a secondary-storage variant of our technique in PostgreSQL. This variant does not need to materialize the OBDD, but computes, in one scan over the lineage, the probabilities of OBDD fragments and combines them on the fly. Experiments with probabilistic TPC-H data show up to two orders of magnitude improvements when compared with state-of-the-art approaches.