# Database Repairing with Soft Functional Dependencies

arXiv: https://arxiv.org/abs/2009.13821 · HTML: https://mlsanity.com/paper/2009.13821/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Sep 2020.

## Built on by (most cited first, 2 of 2)

- [Cost-Based Semantics for Querying Inconsistent Weighted Knowledge Bases](https://mlsanity.com/paper/2407.20754/) (2024)
- [Stress-Testing Causal Claims via Cardinality Repairs](https://mlsanity.com/paper/2512.02491/) (2025)

## Abstract (arXiv)

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.