Unambiguous Prioritized Repairing of Databases

In its traditional definition, a repair of an inconsistent databaseis a consistent database that differs from the inconsistent onein a “minimal way.” Often, repairs are not equally legiti-mate, as it is desired to prefer one over another; for example,one fact is regarded more reliable than another, or a morerecent fact should be preferred to an earlier one. Motivatedby these considerations, researchers have introduced and in-vestigated the framework of preferred repairs, in the contextof denial constraints and subset repairs. There, a priorityrelation between facts is lifted towards a priority relationbetween consistent databases, and repairs are restricted tothe ones that are optimal in the lifted sense. Three notionsof lifting (and optimal repairs) have been proposed: Pareto,global, and completion.In this paper we investigate the complexity of decidingwhether the priority relation suffices to clean the databaseunambiguously, or in other words, whether there is exactlyone optimal repair. We show that the different lifting se-mantics entail highly different complexities. Under Paretooptimality, the problem is coNP-complete, in data complex-ity, for every set of functional dependencies (FDs), exceptfor the tractable case of (equivalence to) one FD per rela-tion. Under global optimality, one FD per relation is stilltractable, but we establishΠp2-completeness for a relationwith two FDs. In contrast, under completion optimality theproblem is solvable in polynomial time for every set of FDs.In fact, we present a polynomial-time algorithm for arbitraryconflict hypergraphs. We further show that under a generalassumption of transitivity, this algorithm solves the problemeven for global optimality. The algorithm is extremely sim-ple, but its proof of correctness is quite intricate.