The structure of inverses in schema mappings

A schema mapping is a specification that describes how data structured under one schema (the source schema) is to be transformed into data structured under a different schema (the target schema). The notion of an inverse of a schema mapping is subtle, because a schema mapping may associate many target instances with each source instance, and many source instances with each target instance. In PODS 2006, Fagin defined a notion of the inverse of a schema mapping. This notion is tailored to the types of schema mappings that commonly arise in practice (those specified by "source-to-target tuple-generating dependencies", or s-t tgds). We resolve the key open problem of the complexity of deciding whether there is an inverse. We also explore a number of interesting questions, including: What is the structure of an inverse? When is the inverse unique? How many non-equivalent inverses can there be? When does an inverse have an inverse? How big must an inverse be? Surprisingly, these ...

• Type: Journal
• Year: 2010
• Where: JACM
• Authors: Ronald Fagin, Alan Nash
• Keywords: Algorithms, JACM 2010, S-t Tgds, Schema Mapping, Target Instance