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 NPhard. 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.

The consistency extractor system: Answer set programs for consistent query answering in databases

“…In [11,14,37,45,58,59] minimality associated to repairs is based on the cardinality of the set of updates, i.e. changes of attributes values (as opposed to whole tuples).…”

CrowdAidRepair: A Crowd-Aided Interactive Data Repairing Method

“…The traditional category of methods relies on a variety of constraints including FDs [1,11], CFDs [4], Integrity Constraints [9] and Inclusion Dependencies (INCs) [1] to detect inconsistency (or conflicts) between data aroused by erroneous data, and then work on resolving all the conflicts with expecting to fix all erroneous data in this way [2,8,9]. For general textual databases, most work in this category use FD/CFDs for repairing as they are the constraints within a single relational table, while some other work uses INCs for repairing between multiple relational tables.…”

“…For general textual databases, most work in this category use FD/CFDs for repairing as they are the constraints within a single relational table, while some other work uses INCs for repairing between multiple relational tables. Usually, this category of methods can e↵ectively detect a large percent of erroneous data involved in the identified conflicts in a wide range of databases, but to repair these errors and resolve the conflicts, some work tends to make the least changes to the data set [2,9], while others prefer to make the most likely correct changes based on some simple prediction model [8,12]. However, neither criterion can have all errors modified correctly.…”

“…So far, various data repairing solutions have been developed to automatically detect and repair erroneous data in databases [12]. The main stream of rule-based solutions [2,8,9] rely on a variety of quality rules such as FD/CFDs [1,4,11] to detect violations and conflicts between data. By resolving these violations and conflicts, they expect to fix the erroneous data.…”

“…When a conflict happens between values, some values should be modified in order to resolve the conflict. In order to resolve all the conflicts in a database, some works tend to make the least changes to the data set [2,9], while others prefer to make the most likely correct changes based on some simple prediction model [8,12]. For example in Fig.…”