The Complexity of Counting Problems Over Incomplete Databases

We study the complexity of various fundamental counting problems that arise in the context of incomplete databases, i.e., relational databases that can contain unknown values in the form of labeled nulls. Specifically, we assume that the domains of these unknown values are finite and, for a Boolean query q , we consider the following two problems: Given as input an incomplete database D , (a) return the number of completions of D that satisfy q ; or (b) return the number of valuations of the nulls of D yielding a completion that satisfies q . We obtain dichotomies between #P-hardness and polynomial-time computability for these problems when q is a self-join–free conjunctive query and study the impact on the complexity of the following two restrictions: (1) every null occurs at most once in D (what is called Codd tables ); and (2) the domain of each null is the same. Roughly speaking, we show that counting completions is much harder than counting valuations: For instance, while the latter is always in #P, we prove that the former is not in #P under some widely believed theoretical complexity assumption. Moreover, we find that both (1) and (2) can reduce the complexity of our problems. We also study the approximability of these problems and show that, while counting valuations always has a fully polynomial-time randomized approximation scheme (FPRAS), in most cases counting completions does not. Finally, we consider more expressive query languages and situate our problems with respect to known complexity classes.

Query Games in Databases

Database tuples can be seen as players in the game of jointly realizing the answer to a query. Some tuples may contribute more than others to the outcome, which can be a binary value in the case of a Boolean query, a number for a numerical aggregate query, and so on. To quantify the contributions of tuples, we use the Shapley value that was introduced in cooperative game theory and has found applications in a plethora of domains. Specifically, the Shapley value of an individual tuple quantifies its contribution to the query. We investigate the applicability of the Shapley value in this setting, as well as the computational aspects of its calculation in terms of complexity, algorithms, and approximation.

Refining Boolean queries to identify relevant studies for systematic review updates

Objective Systematic reviews are important in health care but are expensive to produce and maintain. The authors explore the use of automated transformations of Boolean queries to improve the identification of relevant studies for updates to systematic reviews. Materials and Methods A set of query transformations, including operator substitution, query expansion, and query reduction, were used to iteratively modify the Boolean query used for the original systematic review. The most effective transformation at each stage is identified using information about the studies included and excluded from the original review. A dataset consisting of 22 systematic reviews was used for evaluation. Updated queries were evaluated using the included and excluded studies from the updated version of the review. Recall and precision were used as evaluation measures. Results The updated queries were more effective than the ones used for the original review, in terms of both precision and recall. The overall number of documents retrieved was reduced by more than half, while the number of relevant documents found increased by 10.3%. Conclusions Identification of relevant studies for updates to systematic reviews can be carried out more effectively by using information about the included and excluded studies from the original review to produce improved Boolean queries. These updated queries reduce the overall number of documents retrieved while also increasing the number of relevant documents identified, thereby representing a considerable reduction in effort required by systematic reviewers.