Gösta Grahne
ABSTRACT
The inversion of data exchange mappings is one of the thorniest issues in data exchange. In this paper we study inverse data exchange from a novel perspective. Previous work has dealt with the static problem of finding a target-to-source mapping that captures the "inverse" of a source-to-target data exchange mapping. As we will show this approach has some drawbacks when it come actually applying the inverse mapping in order to recover a source instance from a materialized target instance. More specifically (1): As is well known, the inverse mappings have to be expressed in a much more powerful language than the mappings they invert. (2): There are simple cases where a source instance computed by the inverse mapping misses sound information that one may easily obtain when the particular target instance is available. (3): In some cases the inverse mapping can introduce unsound information in the recovered source instance.
To overcome these drawbacks we focus on the dynamic problem of recovering the source instance using the source-to-target mapping as well as a given target instance. Similarly to the problem of finding "good" target instances in forward data exchange, we look for "good" source instances to restore, i.e. to materialize. For this we introduce a new semantics to capture instance based recovery. We then show that given a target instance and a source-to-target mapping expressed as set of tuple generating dependencies, there are chase-based algorithms to compute a representative finite set of source instances that can be used to get certain answers to any union of conjunctive source queries. We also show that the instance based source recovery problem unfortunately is coNP-complete. We therefore present a polynomial time algorithm that computes a "small" set of source instances that can be used to get sound certain answers to any union of conjunctive source queries. This algorithm is then extended to extract more sound information for the case when only conjunctive source queries are allowed.
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Index Terms
- Recovering Exchanged Data
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