Computing Optimal Repairs for Functional Dependencies

TL;DR

This paper analyzes the complexity of repairing inconsistent databases with functional dependencies, providing polynomial algorithms for some cases and proving NP-hardness and APX-completeness for others, thus establishing a complexity dichotomy.

Contribution

It introduces a polynomial-time algorithm for certain FD sets, proves NP-hardness and APX-completeness for others, and generalizes a previous dichotomy in database repair complexity.

Findings

Polynomial-time algorithm for some FD sets

NP-hardness and APX-completeness results for others

Establishment of a complexity dichotomy for optimal repairs

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 S-repair. 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.