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Reverse data exchange: coping with nulls

Published:29 June 2009Publication History

ABSTRACT

An inverse of a schema mapping M is intended to "undo" what M does, thus providing a way to perform "reverse" data exchange. In recent years, three different formalizations of this concept have been introduced and studied, namely, the notions of an inverse of a schema mapping, a quasi-inverse of a schema mapping, and a maximum recovery of a schema mapping. The study of these notions has been carried out in the context in which source instances are restricted to consist entirely of constants, while target instances may contain both constants and labeled nulls. This restriction on source instances is crucial for obtaining some of the main technical results about these three notions, but, at the same time, limits their usefulness, since reverse data exchange naturally leads to source instances that may contain both constants and labeled nulls.

We develop a new framework for reverse data exchange that supports source instances that may contain nulls, thus overcoming the semantic mismatch between source and target instances of the previous formalizations. The development of this new framework requires a careful reformulation of all the important notions, including the notions of the identity schema mapping, inverse, and maximum recovery. To this effect, we introduce the notions of extended identity schema mapping, extended inverse, and maximum extended recovery, by making systematic use of the homomorphism relation on instances. We give results concerning the existence of extended inverses and of maximum extended recoveries, and results concerning their applications to reverse data exchange and query answering. Moreover, we show that maximum extended recoveries can be used to capture in a quantitative way the amount of information loss embodied in a schema mapping specified by source-to-target tuple-generating dependencies.

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          • Published in

            cover image ACM Conferences
            PODS '09: Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
            June 2009
            298 pages
            ISBN:9781605585536
            DOI:10.1145/1559795
            • General Chair:
            • Jan Paredaens,
            • Program Chair:
            • Jianwen Su

            Copyright © 2009 ACM

            Publisher

            Association for Computing Machinery

            New York, NY, United States

            Publication History

            • Published: 29 June 2009

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