The use of transitively irreducible kernels of full families of functional dependencies in logical data base design

  • Peter Kandzia
  • Margret Mangelmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 100)


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.


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  1. /1/.
    Armstrong, W.W.: Dependency Structures of Database Relationships, Proc. IFIP 74, North Holland, 1974, pp. 580–583.Google Scholar
  2. /2/.
    Beeri, C., Bernstein, P.A.: Computational Problems Related to the Design of Normal Form Relational Schemas, ACM TODS Vol. 4, No. 1, 1979.Google Scholar
  3. /3/.
    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.Google Scholar
  4. /4/.
    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.Google Scholar
  5. /5/.
    Codd, E.F.: Recent investigations in relational data base systems, IFIP 74 (North-Holland, 1974), pp. 1017–1021.Google Scholar
  6. /6/.
    Date, C.J.: An Introduction to Database Systems, (Addison-Wesley, 1977).Google Scholar
  7. /7/.
    Fagin, R.: Dependency in a relational database and propositional logic, IBM Res. Rep. RJ 1776 (1976).Google Scholar
  8. /8/.
    Lucchesi, C.L., Osborn, S.L.: Candidate Keys for Relations, Journal of Computer and System Sciences, Vol. 17, No. 2, October 1978.Google Scholar
  9. /9/.
    Noltemeier, H.: Transitive Irreduzibilität in: Mühlbacher, J. (ed.), Datenstrukturen, Graphen, Algorithmen, Carl-Hanser-Verlag, München, 1978.Google Scholar
  10. /10/.
    Noltemeier, H.: Graphentheoretische Modelle und Methoden, GI-Fachtagung "Formale Modelle für Informationssysteme", Tutzing, 1979 Informatik-Fachberichte 21, Springer-Verlag.Google Scholar
  11. /11/.
    Osborn, S.L.: Testing for Existence of a Covering Boyce-Codd Normal Form, Information Processing Letters, Vol. 8, No. 1, 1979, pp. 11–14.Google Scholar
  12. /12/.
    Pichat, E., Delobel, C.: Designing a 3rd Normal Form Relational Data Base Schema Workshop: Formal Bases for Data Bases Toulouse, 1979.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Peter Kandzia
    • 1
  • Margret Mangelmann
    • 1
  1. 1.Institut für Informatik und Praktische MathematikChristian-Albrecht-Universität KielKiel 1

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