On the Complexity of Deriving Schema Mappings from Database Instances

We introduce a theoretical framework for discovering relationships between two database instances over distinct and unknown schemata. This framework is grounded in the context of data exchange. We formalize the problem of understanding the relationship between two instances as that of obtaining a schema mapping (a set of sentences in some logical language) so that a minimum repair of this mapping provides a perfect description of the target instance given the source instance. We show that this definition yields “intuitive” results when applied on database instances derived from each other by basic operations (selections, projections, joins, and so forth). We study the complexity of decision problems related to this optimality notion in the context of different logical languages (e.g., full acyclic tuple-generating dependencies) and show that, even in very restricted cases, the problem is of high complexity