Database Repairing with Soft Functional Dependencies

ACM Transactions on Database Systems, vol. 49, pp. 1–34

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 finding an optimal subset for the more general soft semantics. The work described in this manuscript makes significant progress in that direction. In addition to general insights about the hardness and approximability of the problem, we present algorithms for two special cases (and some generalizations thereof): 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. For these special cases, we also investigate the complexity of additional computational tasks that arise when the soft constraints are used as a means to represent a probabilistic database in the case of a probabilistic unclean database.

Authors 5

1. Nofar Carmeli

   Centre National de la Recherche Scientifique · Institut national de recherche en sciences et technologies du numérique · Laboratoire d'Informatique, de Robotique et de Microélectronique de Montpellier

   Affiliation as printed

   Inria, LIRMM, Univ Montpellier, CNRS, Montpellier, France

2. Martin Grohe Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Aachen, Germany

3. Benny Kimelfeld

   Technion – Israel Institute of Technology

   Affiliation as printed

   Technion – Israel Institute of Technology, Haifa, Israel

   Technion - Israel Institute of Technology [Haifa] (Technion City, Haifa 3200003 - Israel)

4. Ester Livshits

   University of Edinburgh

   Affiliation as printed

   University of Edinburgh, Edinburgh, UK

   Edin. - University of Edinburgh (Old College South Bridge Edinburgh EH8 9YL - United Kingdom)

5. Muhammad Tibi

   Technion – Israel Institute of Technology

   Affiliation as printed

   Technion – Israel Institute of Technology, Haifa, Israel

   Technion - Israel Institute of Technology [Haifa] (Technion City, Haifa 3200003 - Israel)