Database Repairing with Soft Functional Dependencies

Authors Nofar Carmeli, Martin Grohe, Benny Kimelfeld, Ester Livshits, Muhammad Tibi

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Author Details

Nofar Carmeli
  • Technion - Israel Institute of Technology, Haifa, Israel
Martin Grohe
  • RWTH Aachen University, Germany
Benny Kimelfeld
  • Technion - Israel Institute of Technology, Haifa, Israel
Ester Livshits
  • Technion - Israel Institute of Technology, Haifa, Israel
Muhammad Tibi
  • Technion - Israel Institute of Technology, Haifa, Israel


The authors are very grateful to Alessio Conte and Peter Lindner for insightful discussions about the work described in this paper.

Cite AsGet BibTex

Nofar Carmeli, Martin Grohe, Benny Kimelfeld, Ester Livshits, and Muhammad Tibi. Database Repairing with Soft Functional Dependencies. In 24th International Conference on Database Theory (ICDT 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 186, pp. 16:1-16:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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 finding an optimal subset for 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Incomplete, inconsistent, and uncertain databases
  • Information systems → Data cleaning
  • Database inconsistency
  • database repairs
  • integrity constraints
  • soft constraints
  • functional dependencies


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