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Mappings between different representations of data are the essential building blocks for
many information integration tasks. A schema mapping is a high-level specification
of the relationship between two schemas, and represents a useful abstraction that specifies
how the data from a source format can be transformed into a target format. The development
of schema mappings is laborious and time-consuming, even in the presence of tools that facilitate
this development. At the same time, schema evolution inevitably causes the invalidation of
the existing schema mappings (since their schemas change). Providing tools and methods that
can facilitate the adaptation and reuse of the existing schema mappings in the context of the
new schemas is an important research problem.
In this chapter, we show how two fundamental operators on schema mappings, namely
composition and inversion, can be used to address the mapping adaptation problem
in the context of schema evolution. We illustrate the applicability of the two operators in various
concrete schema evolution scenarios, and we survey the most important developments on the
semantics, algorithms and implementation of composition and inversion. We also discuss the
main research questions that still remain to be addressed.