Abstract
In a paper of H. Noltemeier there is a remark that normalization processes in Codd's relational data model lead to the problem of determining transitively irreducible kernels in graphs. This idea, in particular properties of trans. irr. kernels of full families of functional dependencies (FDs) are investigated. It is shown that such kernels have some kind of coset structure which allows to restrict the investigations to the so-called main classes. Moreover, the main classes have a clear structure, determined among others by one maximal and some minimal elements, specified by certain formulae. The max. and minimal elements of the main classes contain all important information on the full families of FDs. The result can be employed as a common framework for algorithms essential in logical data base design.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Armstrong, W.W.: Dependency Structures of Database Relationships, Proc. IFIP 74, North Holland, 1974, pp. 580–583.
Beeri, C., Bernstein, P.A.: Computational Problems Related to the Design of Normal Form Relational Schemas, ACM TODS Vol. 4, No. 1, 1979.
Biskup, J., Dayal, U., Bernstein, P.A.: Synthesizing Independent Database Schemas, Proc. ACM-SIGMOD, Int. Conf. on Management of Data, P.A. Bernstein ed., 1979, pp. 143–151.
Codd, E.F.: Further normalization of the relational data base model, in: R. Rustin (ed.), Courant Computer Science Symposium 6, Data Base Systems (Prentice-Hall, 1971) pp. 33–64.
Codd, E.F.: Recent investigations in relational data base systems, IFIP 74 (North-Holland, 1974), pp. 1017–1021.
Date, C.J.: An Introduction to Database Systems, (Addison-Wesley, 1977).
Fagin, R.: Dependency in a relational database and propositional logic, IBM Res. Rep. RJ 1776 (1976).
Lucchesi, C.L., Osborn, S.L.: Candidate Keys for Relations, Journal of Computer and System Sciences, Vol. 17, No. 2, October 1978.
Noltemeier, H.: Transitive Irreduzibilität in: Mühlbacher, J. (ed.), Datenstrukturen, Graphen, Algorithmen, Carl-Hanser-Verlag, München, 1978.
Noltemeier, H.: Graphentheoretische Modelle und Methoden, GI-Fachtagung "Formale Modelle für Informationssysteme", Tutzing, 1979 Informatik-Fachberichte 21, Springer-Verlag.
Osborn, S.L.: Testing for Existence of a Covering Boyce-Codd Normal Form, Information Processing Letters, Vol. 8, No. 1, 1979, pp. 11–14.
Pichat, E., Delobel, C.: Designing a 3rd Normal Form Relational Data Base Schema Workshop: Formal Bases for Data Bases Toulouse, 1979.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1981 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kandzia, P., Mangelmann, M. (1981). The use of transitively irreducible kernels of full families of functional dependencies in logical data base design. In: Noltemeier, H. (eds) Graphtheoretic Concepts in Computer Science. WG 1980. Lecture Notes in Computer Science, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10291-4_14
Download citation
DOI: https://doi.org/10.1007/3-540-10291-4_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10291-5
Online ISBN: 978-3-540-38435-9
eBook Packages: Springer Book Archive