Database Repairing with Soft Functional Dependencies

DROPS (Schloss Dagstuhl – Leibniz Center for Informatics)

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. 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.

Authors 5

1. Nofar Carmeli

   Technion – Israel Institute of Technology

   Affiliation as printed

   Technion - Israel Institute of Technology, Haifa, Israel

   Technion – Israel Institute of Technology, Haifa, Israel

2. Martin Grohe Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Germany

   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, Israel

4. Ester Livshits

   Technion – Israel Institute of Technology

   Affiliation as printed

   Technion - Israel Institute of Technology, Haifa, Israel

   Technion – Israel Institute of Technology, Haifa, Israel

5. Muhammad Tibi

   Technion – Israel Institute of Technology

   Affiliation as printed

   Technion - Israel Institute of Technology, Haifa, Israel

   Technion – Israel Institute of Technology, Haifa, Israel