We study the problem of repairing an inconsistent database that violates a set of functional dependencies by making the smallest possible value modifications. For an inconsistent database, we define an optimum repair as a database that satisfies the functional dependencies, and minimizes, among all repairs, a distance measure that depends on the number of corrections made in the database and the weights of tuples modified. We show that like other versions of the repair problem, checking the existence of a repair within a certain distance of a database is NP-complete. We also show that finding a constant-factor approximation for the optimum repair for any set of functional dependencies is NPhard. Furthermore, there is a small constant and a set of functional dependencies, for which finding an approximate solution for the optimum repair within the factor of that constant is also NP-hard. Then we present an approximation algorithm that for a fixed set of functional dependencies and an arbitrary input inconsistent database, produces a repair whose distance to the database is within a constant factor of the optimum repair distance. We finally show how the approximation algorithm can be used in data cleaning using a recent extension to functional dependencies, called conditional functional dependencies.

Matching dependencies were recently introduced as declarative rules for data cleaning and entity resolution. Enforcing a matching dependency on a database instance identifies the values of some attributes for two tuples, provided that the values of some other attributes are sufficiently similar. Assuming the existence of matching functions for making two attributes values equal, we formally introduce the process of cleaning an instance using matching dependencies, as a chase-like procedure. We show that matching functions naturally introduce a lattice structure on attribute domains, and a partial order of semantic domination between instances. Using the latter, we define the semantics of clean query answering in terms of certain/possible answers as the greatest lower bound/least upper bound of all possible answers obtained from the clean instances. We show that clean query answering is intractable in some cases. Then we study queries that behave monotonically w.r.t. semantic domination order, and show that we can provide an under/over approximation for clean answers to monotone queries. Moreover, non-monotone positive queries can be relaxed into monotone queries.

Matching dependencies were recently introduced as declarative rules for data cleaning and entity resolution. Enforcing a matching dependency on a database instance identifies the values of some attributes for two tuples, provided that the values of some other attributes are sufficiently similar. Assuming the existence of matching functions for making two attributes values equal, we formally introduce the process of cleaning an instance using matching dependencies, as a chase-like procedure. We show that matching functions naturally introduce a lattice structure on attribute domains, and a partial order of semantic domination between instances. Using the latter, we define the semantics of clean query answering in terms of certain/possible answers as the greatest lower bound/least upper bound of all possible answers obtained from the clean instances. We show that clean query answering is intractable in some cases. Then we study queries that behave monotonically w.r.t. semantic domination order, and show that we can provide an under/over approximation for clean answers to monotone queries. Moreover, non-monotone positive queries can be relaxed into monotone queries.

Having a database design that avoids redundant information and update anomalies is the main goal of normalization techniques. Ideally, data as well as constraints should be preserved. However, this is not always achievable: while BCNF eliminates all redundancies, it may not preserve constraints, and 3NF, which achieves dependency preservation, may not always eliminate all redundancies. Our first goal is to investigate how much redundancy 3NF tolerates in order to achieve dependency preservation. We apply an information-theoretic measure and show that only prime attributes admit redundant information in 3NF, but their information content may be arbitrarily low. Then we study the possibility of achieving both redundancy elimination and dependency preservation by a hierarchical representation of relational data in XML. We provide a characterization of cases when an XML normal form called XNF guarantees both. Finally, we deal with dependency preservation in XML and show that like in the relational case, normalizing XML documents to achieve non-redundant data can result in losing constraints.

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