Counting and Enumerating (Preferred) Database Repairs

In the traditional sense, a subset repair of an inconsistent database refers to a consistent subset of facts (tuples) that is maximal under set containment. Preferences between pairs of facts allow to distinguish a set of preferred repairs based on relative reliability (source credibility, extraction quality, recency, etc.) of data items. Previous studies explored the problem of categoricity, where one aims to determine whether preferences suffice to repair the database unambiguously, or in other words, whether there is precisely one preferred repair. In this paper we study the ability to quantify ambiguity, by investigating two classes of problems. The first is that of counting the number of subset repairs, both preferred (under various common semantics) and traditional. We establish dichotomies in data complexity for the entire space of (sets of) functional dependencies. The second class of problems is that of enumerating (i.e., generating) the preferred repairs. We devise enumeration algorithms with efficiency guarantees on the delay between generated repairs, even for constraints represented as general conflict graphs or hypergraphs.