Computing Optimal Repairs for Functional Dependencies

Abstract

We investigate the complexity of computing an optimal repair of an inconsistent database, in the case where integrity constraints are Functional Dependencies (FDs). We focus on two types of repairs: an optimal subset repair (optimal S-repair) that is obtained by a minimum number of tuple deletions, and an optimal update repair (optimal U-repair) that is obtained by a minimum number of value (cell) updates. For computing an optimal S-repair, we present a polynomial-time algorithm that succeeds on certain sets of FDs and fails on others. We prove the following about the algorithm. When it succeeds, it can also incorporate weighted tuples and duplicate tuples. When it fails, the problem is NP-hard, and in fact, APX-complete (hence, cannot be approximated better than some constant). Thus, we establish a dichotomy in the complexity of computing an optimal Srepair. We present general analysis techniques for the complexity of computing an optimal U-repair, some based on the dichotomy for S-repairs. We also draw a connection to a past dichotomy in the complexity of finding a "most probable database" that satisfies a set of FDs with a single attribute on the left hand side; the case of general FDs was left open, and we show how our dichotomy provides the missing generalization and thereby settles the open problem.

Capuchin: Causal Database Repair for Algorithmic Fairness

“…The problem has been studied extensively in database theory for various classes of constraints Γ. It is NP-hard even when D consists of a single relation (as it does in our paper) and Γ consists of functional dependencies [27]. In our setting, Γ consists of conditional independence statements, and it remains NP-hard, as we show in Sec.…”

On Multiple Semantics for Declarative Database Repairs

“…Regarding methods of data repair, previous works have considered two main approaches: (1) repairing attribute values in cells [6,11,29,33,44] and (2) tuple deletion [10,33,34]; our work focuses on the latter. A major advantage of our approach is the ability to perform cascade deletions over multiple relations in the database while following different well-defined semantics (and the admin may choose which one to follow based on the application scenario).…”

“…A major advantage of our approach is the ability to perform cascade deletions over multiple relations in the database while following different well-defined semantics (and the admin may choose which one to follow based on the application scenario). Similar to our independent semantics, a common objective for data repairs is to change the database in the minimal way that will make it consistent with the constraints [5,19,33]. In some scenarios a good repair can be obtained by changing values in the database and the metric of minimal changes may not work well [44].…”

“…Many of these have focused on the desideratum of minimum cardinality, i.e., repairing the database while making the minimum number of changes [5,19,34]. In particular, when the repair only involves tuple deletion [10,33,34], this desideratum takes center stage since a näive repair could simply delete the entire database in order to repair it. Such repairs are commonly used with classes of constraints such as Denial Constraints (DCs) [10,11], SQL deletion triggers [22], and causal dependencies [46].…”

Cleaning Denial Constraint Violations through Relaxation

“…To capture partial knowledge of the rules and the data, we clean data by providing probabilistic fixes. Then, using our solution once all rules are known and given the probabilistic suggestions, we can either use inference [23,29,36] when master data exist, or have humans fix the errors in the query results. Inference approaches over the probabilistic data are complementary and out of the scope of this work.…”