The data mapping problem is to discover effective mappings between structured representations of data. These mappings are the basic ?glue? for facilitating large-scale ad-hoc information sharing between autonomous peers in a dynamic environment. Automating their discovery is one of the fundamental unsolved challenges for information integration and sharing on the Web. We outline a general approach to automating the discovery of mappings between relational data sources which leverages new perspectives on the data mapping problem and report on a prototype implementation. Our approach utilizes heuristic search within a space delineated by basic relational transformation operators. A further novelty of our approach is that these operators include data to metadata transformations (and vice versa), allowing a generalization of previous solutions such as token-based schema matching.