Abstract
In the relational database model, it is important to obtain a set of relations which are normalized. In order to reduce the total number of normalized relations, relations with more than one key must be considered. Keys in the same relation are called equivalent. Bernstein has developed an algorithm to obtain a minimum relation set using the key equivalence concept. The major results of this paper are that (1) problems of the Bernstein's algorithm are pointed out and algorithms to handle these problems are shown and (2) for several normalization classes algorithms for minimum schema design are given considering the key equivalence. The following approaches are used in this paper; (1) a new definition of key equivalence, (2) minimization techniques of logic functions (prime implicant generation, a generalized minimum cover problem), (3) the idea used in the minimization of incompletely specified sequential machines.
Preview
Unable to display preview. Download preview PDF.
References
E.F. Codd,"A relational model of data for large shared data banks," CACM,vol.13,no.6, pp.377–387, June 1970.
E.F.Codd,"Further normalization of the data base relational model," in Data Base Systems, R. Rustin, Ed., Prentice-Hall, 1972.
C. Delobel and R.G. Casey,"Decomposition of a data base and the theory of Boolean switching functions," IBM J.Res. Develop. vol.17,no.5, pp.374–386, Sept. 1972.
C.P. Wang and H.H. Wedekind,"Segment synthesis in logical data base design," IBM J.Res. Develop., vol.19, no.1, pp.71–77, Jan. 1975.
P.A. Bernstein,"Synthesizing third normal form relations from functional dependencies," ACM Trans.Database Systems, vol.1,no.4, pp.277–298, Dec. 1976.
W.W. Armstrong, "Dependency structures of data base relationships," Information processing 74, North-Holland Pub. Co., Amsterdam, pp.580–583, 1974.
P.A. Bernstein,"A comment on segment synthesis in logical data base design," IBM J.Res. Develop., vol.20,no.4, p.412, July 1976.
R. Fagin,"Dependency in a relational database and propositional logic," IBM J.Res. Develop., vol.21, no.6, pp.534–544, Nov. 1977.
R. Fagin,"Multivalued dependencies and a new normal form for relational databases," ACM Trans.Database Systems, vol.2,no.3, pp.262–278, Dec. 1977.
R.Fagin,"The decomposition versus the synthetic approach to relational batabase design," Proceedings of the Third International Conference on Very Large Data Bases, pp.441–446, Oct. 1977.
C, Zaniolo, "Analysis and design of relational schemata for batabase systems," (Ph,D thesis), Computer Science Department, UCLA, Technical Report UNCLA-ENG-7769, July 1976.
Y.Kambayashi, K.Tanaka and S.Yajima,"A relational data language with simplified binary relation handling capability," Proceedings of the Third International Conference on Very Large Data Bases, pp.338–350, Oct. 1977.
S. Muroga,"Threshold logic and its application," John Wiley and Sons, New York, 1971.
Y.Kambayashi,"Equivalent key problem of the relational database model," The Institute of Electronics and Communication Engineers of Japan, SIGAL(Automata and Languages) Record, AL 77–22, July 1977 (in Japanese).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1979 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kambayashi, Y. (1979). Equivalent key problem of the relational database model. In: Blum, E.K., Paul, M., Takasu, S. (eds) Mathematical Studies of Information Processing. Lecture Notes in Computer Science, vol 75. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09541-1_27
Download citation
DOI: https://doi.org/10.1007/3-540-09541-1_27
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09541-5
Online ISBN: 978-3-540-35010-1
eBook Packages: Springer Book Archive