Database Repairing with Soft Functional Dependencies

TL;DR

This paper investigates the complexity of repairing databases with soft functional dependencies, providing new insights into hardness, approximability, and algorithms for specific cases like single dependencies and bipartite matchings.

Contribution

It advances understanding of the computational complexity of soft dependency repairs and introduces algorithms for special cases such as single functional dependencies and bipartite matchings.

Findings

Hardness and approximability results for soft dependency repair problems.

Algorithms for single functional dependency repair.

Algorithm for bipartite matching with penalties for violations.

Abstract

A common interpretation of soft constraints penalizes the database for every violation of every constraint, where the penalty is the cost (weight) of the constraint. A computational challenge is that of finding an optimal subset: a collection of database tuples that minimizes the total penalty when each tuple has a cost of being excluded. When the constraints are strict (i.e., have an infinite cost), this subset is a "cardinality repair" of an inconsistent database; in soft interpretations, this subset corresponds to a "most probable world" of a probabilistic database, a "most likely intention" of a probabilistic unclean database, and so on. Within the class of functional dependencies, the complexity of finding a cardinality repair is thoroughly understood. Yet, very little is known about the complexity of this problem in the more general soft semantics. This paper makes a significant progress in this direction. In addition to general insights about the hardness and approximability of the problem, we present algorithms for two special cases: a single functional dependency, and a bipartite matching. The latter is the problem of finding an optimal "almost matching" of a bipartite graph where a penalty is paid for every lost edge and every violation of monogamy.