Uncertainty Annotated Databases - A Lightweight Approach for Approximating Certain Answers (extended version)

Certain answers are a principled method for coping with uncertainty that arises in many practical data management tasks. Unfortunately, this method is expensive and may exclude useful (if uncertain) answers. Thus, users frequently resort to less principled approaches to resolve the uncertainty. In this paper, we propose Uncertainty Annotated Databases (UA-DBs), which combine an under- and over-approximation of certain answers to achieve the reliability of certain answers, with the performance of a classical database system. Furthermore, in contrast to prior work on certain answers, UA-DBs achieve a higher utility by including some (explicitly marked) answers that are not certain. UA-DBs are based on incomplete K-relations, which we introduce to generalize the classical set-based notions of incomplete databases and certain answers to a much larger class of data models. Using an implementation of our approach, we demonstrate experimentally that it efficiently produces tight approximations of certain answers that are of high utility

New Results for the Complexity of Resilience for Binary Conjunctive Queries with Self-Joins

The resilience of a Boolean query is the minimum number of tuples that need to be deleted from the input tables in order to make the query false. A solution to this problem immediately translates into a solution for the more widely known problem of deletion propagation with source-side effects. In this paper, we give several novel results on the hardness of the resilience problem for $\textit{binary conjunctive queries with self-joins}$ (i.e. conjunctive queries with relations of maximal arity 2) with one repeated relation. Unlike in the self-join free case, the concept of triad is not enough to fully characterize the complexity of resilience. We identify new structural properties, namely chains, confluences and permutations, which lead to various $NP$-hardness results. We also give novel involved reductions to network flow to show certain cases are in $P$. Overall, we give a dichotomy result for the restricted setting when one relation is repeated at most 2 times, and we cover many of the cases for 3. Although restricted, our results provide important insights into the problem of self-joins that we hope can help solve the general case of all conjunctive queries with self-joins in the future.Comment: 23 pages, 19 figures, included a new sectio