On approximating optimum repairs for functional dependency violations

Abstract

We study the problem of repairing an inconsistent database that violates a set of functional dependencies by making the smallest possible value modifications. For an inconsistent database, we define an optimum repair as a database that satisfies the functional dependencies, and minimizes, among all repairs, a distance measure that depends on the number of corrections made in the database and the weights of tuples modified. We show that like other versions of the repair problem, checking the existence of a repair within a certain distance of a database is NP-complete. We also show that finding a constant-factor approximation for the optimum repair for any set of functional dependencies is NP-hard. Furthermore, there is a small constant and a set of functional dependencies, for which finding an approximate solution for the optimum repair within the factor of that constant is also NP-hard. Then we present an approximation algorithm that for a fixed set of functional dependencies and an arbitrary input inconsistent database, produces a repair whose distance to the database is within a constant factor of the optimum repair distance. We finally show how the approximation algorithm can be used in data cleaning using a recent extension to functional dependencies, called conditional functional dependencies.