ABSTRACT
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). Although the notion of an inverse of a schema mapping is important, the exact definition of an inverse mapping is somewhat elusive. This is because a schema mapping may associate many target instances with each source instance, and many source instances with each target instance. Based on the notion that the composition of a mapping and its inverse is the identity, we give a formal definition for what it means for a schema mapping M′ to be an inverse of a schema mapping M for a class S of source instances. We call such an inverse an S-inverse. A particular case of interest arises when S is the class of all instances, in which case an S-inverse is a global inverse. We focus on the important and practical case of schema mappings defined by source-to-target tuple-generating dependencies, and uncover a rich theory. When S is defined by a set of dependencies with a finite chase, we show how to construct an S-inverse when one exists. In particular, we show how to construct a global inverse when one exists. Given M and M′, we show how to define the largest class S such that M′ is an S-inverse of M.
- C. Beeri and M. Y. Vardi. A Proof Procedure for Data Dependencies. Journal of the Association for Computing Machinery (JACM), 31(4):718--741, 1984. Google ScholarDigital Library
- P. A. Bernstein. Applying Model Management to Classical Meta-Data Problems. In Conference on Innovative Data Systems Research (CIDR), pages 209--220, 2003.Google Scholar
- R. Fagin. Generalized First-Order Spectra and Polynomial-Time Recognizable Sets. In R. M. Karp, editor, Complexity of Computation, SIAM-AMS Proceedings, Vol. 7, pages 43--73, 1974.Google Scholar
- R. Fagin. Multivalued dependencies and a new normal form for relational databases. ACM Transactions on Database Systems (TODS), 2(3):262--278, Sept. 1977. Google ScholarDigital Library
- R. Fagin, P. G. Kolaitis, R. J. Miller, and L. Popa. Data Exchange: Semantics and Query Answering. Theoretical Computer Science, pages 89--124, 2005. Google Scholar
- R. Fagin, P. G. Kolaitis, and L. Popa. Data Exchange: Getting to the Core. ACM Transactions on Database Systems (TODS), 30(1):174--210, 2005. Google ScholarDigital Library
- R. Fagin, P. G. Kolaitis, L. Popa, and W.-C. Tan. Composing Schema Mappings: Second-Order Dependencies to the Rescue. In ACM Symposium on Principles of Database Systems (PODS), pages 83--94, 2004. Google ScholarDigital Library
- P. Hell and J. Nešetril. The Core of a Graph. Discrete Mathematics, 109:117--126, 1992. Google ScholarDigital Library
- R. Hull. Relative Information Capacity of Simple Relational Database Schemata. SIAM J. on Computing, 15:856--886, 1986. Google ScholarDigital Library
- M. Lenzerini. Data Integration: A Theoretical Perspective. In ACM Symposium on Principles of Database Systems (PODS), pages 233--246, 2002. Google ScholarDigital Library
- S. Melnik. Generic Model Management: Concepts and Algorithms. Springer, 2004. Google ScholarDigital Library
- S. Melnik, P. Bernstein, A. Halevy, and E. Rahm. Supporting Executable Mappings in Model Management. In ACM SIGMOD International Conference on Management of Data (SIGMOD), pages 167--178, 2005. Google ScholarDigital Library
- N. C. Shu, B. C. Housel, R. W. Taylor, S. P. Ghosh, and V. Y. Lum. EXPRESS: A Data EXtraction, Processing, amd REStructuring System. ACM Transactions on Database Systems (TODS), 2(2):134--174, 1977. Google ScholarDigital Library
- C. Yu and L. Popa. Semantic Adaptation of Schema Mappings when Schemas Evolve. In International Conference on Very Large Data Bases (VLDB), pages 1006--1017, 2005. Google ScholarDigital Library
Index Terms
- Inverting schema mappings
Recommendations
Inverting 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). Although the notion of an inverse of a schema mapping is ...
Quasi-inverses of schema mappings
Schema mappings are high-level specifications that describe the relationship between two database schemas. Two operators on schema mappings, namely the composition operator and the inverse operator, are regarded as especially important. Progress on the ...
Composing schema mappings: Second-order dependencies to the rescue
Special Issue: SIGMOD/PODS 2004A 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). A fundamental problem is composing schema mappings: given ...
Comments