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We describe an algorithm that evaluates queries over probabilistic databases using Mobius' inversion formula in incidence algebras. The queries we consider are unions of conjunctive queries (equivalently: existential, positive First Order sentences), and the probabilistic databases are tuple-independent structures. Our algorithm runs in PTIME on a subset of queries called "safe" queries, and is complete, in the sense that every unsafe query is hard for the class F P #P . The algorithm is very simple and easy to implement in practice, yet it is non-obvious. Mobius' inversion formula, which is in essence inclusion-exclusion, plays a key role for completeness, by allowing the algorithm to compute the probability of some safe queries even when they have some subqueries that are unsafe. We also apply the same lattice-theoretic techniques to analyze an algorithm based on lifted conditioning, and prove that it is incomplete.

In the rank join problem, we are given a set of relations and a scoring function, and the goal is to return the join results with the top K scores. It is often the case in practice that the inputs may be accessed in ranked order and the scoring function is monotonic. These conditions allow for efficient algorithms that solve the rank join problem without reading all of the input. In this article, we present a thorough analysis of such rank join algorithms. A strong point of our analysis is that it is based on a more general problem statement than previous work, making it more relevant to the execution model that is employed by database systems. One of our results indicates that the well-known HRJN algorithm has shortcomings, because it does not stop reading its input as soon as possible. We find that it is NP-hard to overcome this weakness in the general case, but cases of limited query complexity are tractable. We prove the latter with an algorithm that infers provably tight bounds on the potential benefit of reading more input in order to stop as soon as possible. As a result, the algorithm achieves a cost that is within a constant factor of optimal.

This paper introduces COLT (Continuous On-Line Tuning), a novel framework that continuously monitors the workload of a database system and enriches the existing physical design with a set of effective indices. The key idea behind COLT is to gather performance statistics at different levels of detail and to carefully allocate profiling resources to the most promising candidate configurations. Moreover, COLT uses effective heuristics to self-regulate its own performance, lowering its overhead when the system is well tuned and being more aggressive when the workload shifts and it becomes necessary to re-tune the system. We describe an implementation of the proposed framework in the PostgreSQL database system and evaluate its performance experimentally. Our results validate the effectiveness of COLT and demonstrate its ability to modify the system configuration in response to changes in the query load.

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