Tractable Queries with Inequalities on Probabilistic Databases

The problem of efficient evaluation of queries on probabilistic databases has received a great attention in recent years. In this thesis, we introduce novel classes of queries with inequalities (<,≤) that admit tractable evaluation, in the context where query evaluation is #P-hard in general. We also introduce a new kind of hard query that is not captured by previous characterizations. As an application outside database theory, we show that particular tractable instances of our problem capture previously-open problems of counting vertex covers in bipartite chain and convex graphs, for which we can now easily derive efficient algorithms. Our approach to both query evaluation and counting vertex covers is based on a novel syntactical characterization of classes of k-DNFs that capture the lineage of queries from our tractable classes and that can be compiled in at most quadratic time into binary decision diagrams.