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On the correctness of representing extended entity-relationship structures in the relational model
Markowitz V., Shoshani A. ACM SIGMOD Record18(2):430-439,1989.Type:Article
Date Reviewed: 06/01/90

This paper describes a two-step process for deriving a relational schema from an extended entity-relationship (EER) schema. The first step involves generating a canonical representation (Crep) of the EER schema (that is, a set of non-normalized relation schemas in which EER constructs have been mapped to relational constructs according to certain conventions). The second step converts the Crep into a fully normalized relational schema. This process allows certain problems with relational attribute naming to be avoided.

The EER model described in the paper provides for independent entities, aggregations (used to express relationships and weak entities), and generalization. In the generation of a Crep, an independent entity type is mapped to a relation schema whose attributes correspond one for one with the entity type’s attributes. An aggregation type is mapped to a relation schema with attributes for the aggregation proper and for each entity or relationship being aggregated. A subtype maps to a relation schema having attributes for the subtype proper and for each of its supertypes. The Crep represents an EER schema if any state of the former can be uniquely mapped to a state of the latter according to the given mapping conventions.

The second step of the process transforms a Crep schema into a Boyce-Codd Normal Form (BCNF) schema that has an equivalent information capacity. The concept of information capacity is taken from Hull [1] and is based on mappings between pairs of schema instantiations.

The authors discuss previous work on ER-to-relational mappings in some detail and characterize them as being too informal to entertain questions of correctness or equivalence. The paper attempts to provide the formality needed for such questions. The paper’s use of correctness may be misleading, because proofs of transformation correctness normally appeal to some use that is made of the object being transformed (for example, all programs that work on the original object also work on the transformed object), whereas in this paper, correctness is being used basically as a synonym for the mappability of states.


1)

Hull, R.Relative information capacity of simple relational database schemata. In Proceedings of the 3rd ACM SIGACT/SIGMOD Symposium on Principles of Database Systems (Waterloo, Ont., Canada, April 2–4, 1984), ACM, New York, 1986, 97–109.

Reviewer:  W. C. McGee Review #: CR114069

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