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 source instances, in which case an S-inverse is a global inverse. We focus on the important and practical case of schema mappings specified by source-to-target tuple-generating dependencies, and uncover a rich theory. When S is specified 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.
- Arenas, M. 2006. Private communication.Google Scholar
- Beeri, C. and Vardi, M. Y. 1984. A proof procedure for data dependencies. J. Assoc. Comput. Mach. 31, 4, 718--741. Google ScholarDigital Library
- Bernstein, P. A. 2003. Applying model management to classical meta-data problems. In Proceedings of the Conference on Innovative Data Systems Research (CIDR). 209--220.Google Scholar
- Fagin, R. 1974. Generalized first-order spectra and polynomial-time recognizable sets. In Complexity of Computation, SIAM-AMS Proceedings, Vol. 7, R. M. Karp, Ed. SIAM, Philadelphia, PA, 43--73.Google Scholar
- Fagin, R. 1977. Multivalued dependencies and a new normal form for relational databases. ACM Trans. Database Syst. 2, 3 (Sept.), 262--278. Google ScholarDigital Library
- Fagin, R. 2006. Inverting schema mappings. In Proceedings of the ACM Symposium on Principles of Database Systems (PODS). 50--59. Google ScholarDigital Library
- Fagin, R., Kolaitis, P. G., Miller, R. J., and Popa, L. 2005a. Data exchange: Semantics and query answering. Theoret. Comput. Sci. 89--124. Google ScholarDigital Library
- Fagin, R., Kolaitis, P. G., and Popa, L. 2005b. Data exchange: Getting to the core. ACM Trans. Database Sys. 30, 1, 174--210. Google ScholarDigital Library
- Fagin, R., Kolaitis, P. G., Popa, L., and Tan, W.-C. 2005c. Composing schema mappings: Second-order dependencies to the rescue. ACM Trans. Database Sys. 30, 4, 994--1055. Google ScholarDigital Library
- Fagin, R., Kolaitis, P. G., Popa, L., and Tan, W.-C. 2007. Quasi-inverses of schema mappings. In Proceedings of the ACM Symposium on Principles of Database Systems (PODS). 123--132. Google ScholarDigital Library
- Hull, R. 1986. Relative information capacity of simple relational database schemata. SIAM J. Comput. 15, 856--886. Google ScholarDigital Library
- Lenzerini, M. 2002. Data integration: A theoretical perspective. In Porceedings of the ACM Symposium on Principles of Database Systems (PODS). 233--246. Google ScholarDigital Library
- Melnik, S. 2004. Generic Model Management: Concepts and Algorithms. Springer, Berlin, Germany. Google ScholarDigital Library
- Melnik, S., Bernstein, P., Halevy, A., and Rahm, E. 2005. Supporting executable mappings in model management. In Proceedings of the ACM SIGMOD International Conference on Management of Data (SIGMOD). 167--178. Google ScholarDigital Library
- Shu, N. C., Housel, B. C., Taylor, R. W., Ghosh, S. P., and Lum, V. Y. 1977. EXPRESS: A data EXtraction, Processing, and REStructuring System. ACM Trans. Database Syst. 2, 2, 134--174. Google ScholarDigital Library
- Yu, C. and Popa, L. 2005. Semantic adaptation of schema mappings when schemas evolve. In Proceedings of the International Conference on Very Large Data Bases (VLDB). 1006--1017. Google ScholarDigital Library
Index Terms
- Inverting schema mappings
Recommendations
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 ...
Inverting schema mappings
PODS '06: Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systemsA 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 ...
Comments