Abstract
The problem of finding an optimal cover which has possible fewest attributes is NP-complete. It is shown here that an optimal cover can be found, using the notion of mini cover. The minimum Boolean expression of the first Delobel–Casey transform of a set of functional dependencies can be converted into corresponding mini cover, refining classic canonical cover. The relationship between optimal cover and Boolean expression minimization is built, and all theory of Boolean expression minimization can be used to find an optimal cover.
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References
Ausiello, G., D’Atri, A., Sacc, D.: Minimal representation of directed hypergraphs. SIAM J. Comput. 15, 418–431 (1986)
Ausiello, G., D’Atri, A., Sacca, D.: Graph algorithm for functional dependency manipulation. J. ACM 30, 752–766 (1983)
Bernstein, P.A.: Synthesizing third normal form relations from functional dependencies. ACM Trans. Database Syst. 1, 277–298 (1976)
Codd, E.F.: A relational model of data for large shared data banks. Commun. ACM 13, 377–387 (1970)
Cotelea, V.: Problem decomposition method to compute an optimal cover for a set of functional dependencies. Database Syst. J. 2, 17–30 (2011)
Delobel, C., Casey, R.G.: Decomposition of a data base and the theory of Boolean switching functions. IBM J. Res. Dev. 17, 374–386 (1973)
Fagin, R.: Functional Dependencies in a Relational Database and Propositional Logic. IBM J. Res. Dev. 21, 533–544 (1977)
Jain, T.K., Kushwaha, D.S., Misra, A.K.: Optimization of the Quine–McCluskey method for the minimization of the Boolean expressions. In: Fourth International Conference on Autonomic and Autonomous Systems, pp. 165–168. (2008)
Lucchesi, C.L., Osborn, S.L.: Candidate keys for relations. J. Comput. Syst. Sci. 17, 270–279 (1978)
Maier, D.: Minimum covers in the relational database model. J. ACM 27, 664–674 (1980)
Maier, D.: The Theory of Relational Databases, pp. 42–70. Computer Science Press, Rockville, MD (1983)
Mannila, H., Raiha, K.-J.: On the relationship of minimum and optimal covers for a set of functional dependencies. Acta Informatica 20, 143–158 (1983)
McCluskey, E.J.: Minimization of Boolean functions. Bell Syst. Tech. J. 35, 1417–1444 (1956)
McGeer, Patrick C., Sanghavi, Jagesh V., Brayton, Robert K., Sangiovanni-vincentelli, Alberto L.: ESPRESSO-SIGNATURE: A new exact minimizer for logic functions. IEEE Trans. Very Large Scale Integr. Syst. 1, 1–14 (1996)
Peng, X., Xiao, Z.: Comments on problem decomposition method to compute an optimal cover for a set of functional dependencies. Database Syst. J. 4, 50–51 (2013)
Wakerly, J.F.: Digital Design: Principles and Practices, pp. 222–228. Higher Education Press, Beijing (2001)
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The authors would like to thank David Maier for improving the notion of mini cover.
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This work is supported by the constructing program of the key discipline in Huaihua University.
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Peng, X., Xiao, Z. Optimal covers in the relational database model. Acta Informatica 53, 459–468 (2016). https://doi.org/10.1007/s00236-015-0247-9
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DOI: https://doi.org/10.1007/s00236-015-0247-9