Normalization and optimization of schema mappings

Abstract

Schema mappings are high-level specifications that describe the relationship between two database schemas. They are an important tool in several areas of database research, notably in data integration and data exchange. However, a concrete theory of schema mapping optimization including the formulation of optimality criteria and the construction of algorithms for computing optimal schema mappings is completely lacking to date. The goal of this work is to fill this gap. We start by presenting a system of rewrite rules to minimize sets of source-to-target tuple-generating dependencies (st-tgds, for short). Moreover, we show that the result of this minimization is unique up to variable renaming. Hence, our optimization also yields a schema mapping normalization. By appropriately extending our rewrite rule system, we also provide a normalization of schema mappings containing equality-generating targetdependencies (egds). An important application of such a normalization is in the area of defining the semantics of query answering in data exchange, since several definitions in this area depend on the concrete syntactic representation of the st-tgds. This is, in particular, the case for queries with negated atoms and for aggregate queries. The normalization of schema mappings allows us to eliminate the effect of the concrete syntactic representation of the st-tgds from the semantics of query answering. We discuss in detail how our results can be fruitfully applied to aggregate queries.

Closed world data exchange

“…To obtain unique answers for logically equivalent 8 data exchange settings, Gottlob et al [2009] propose to first normalize the data exchange setting as described in their paper, and then apply the semantics. Another approach is to use the semantics developed in Hernich [2010].…”

Leveraging query logs for schema mapping generation in U-MAP

“…For example, [26,19] are two independent approaches for re-writing mappings to generate SQL scripts capable of computing what is known as the core solution for a data exchange problem [12]. Also, [14] shows how schema mappings can be normalized in the same spirit in which relational schemas are normalized. The technique proposed in [18] addresses the situation where key constraints and functional dependencies (egds) hold on the target.…”

Interactive Mapping Specification with Exemplar Tuples

“…• We prove that the generated mappings have irreducible right-hand sides. Combined with redundant mapping elimination, this guarantees that the obtained refined mappings are in normal form [21]. Intuitively, normalized mapping are more self-explanatory and understandable for end-users compared to monolithic canonical mappings.…”