On the complexity of sampling query feedback restricted database repair of functional dependency violations.

An inconsistent database is a database instance violating integrity constraints. A repair of an inconsistent database is a maximal consistent subset. Sampling from the repair space is an alternative approach meeting the needs of many applications. In this paper, we introduce a new class of repair, query feedback restricted repair, based on the feedback on user's witness query. We first map out a picture of both data and combined complexities of repair existence problems under different cases to identify the intractable cases. Especially, we show that if the query is a projection or a union query, then the decision problem is NP-complete; even worse, if the query is a conjunctive query, the decision problem becomes Σ2P-complete. However, we prove that the combined complexity of the repair existence problem is in LOGSPACE when the witness query is a selection-join query, and this conclusion also implies that the combined complexity of side-effect free deletion propagation problem under group-deletion is in LOGSPACE which is not considered in previous works. Additionally, we provide a polynomial random repair sampling algorithm under combined complexity. At last, we revisit the key preserving condition [1] and show that it will simplify the problem, i.e., some cases become tractable for certain key preserving views, as opposed to their counterparts that are not key preserving.