A Note on Lossless Database Decompositions

Abstract It is known that under a wide variety of assumptions a database decomposition is lossless if and only if the database scheme has a lossless join . Biskup, Dayal and Bernstein (1979) have shown that when the given dependencies are functional, the database scheme has a lossless join if and only if one of the relation schemes is a key for the universal scheme. In this note we supply an alternative proof of that characterization. The proof uses tools from the theory of embedded join dependencies and the theory of tuple and equality generating dependencies , but is, nevertheless, much simpler than the previously published proof.

[1]  David Maier,et al.  Testing implications of data dependencies , 1979, SIGMOD '79.

[2]  Catriel Beeri,et al.  Formal Systems for Tuple and Equality Generating Dependencies , 1984, SIAM J. Comput..

[3]  Jorma Rissanen,et al.  Independent components of relations , 1977, TODS.

[4]  David Maier,et al.  The revenge of the JD , 1983, PODS '83.

[5]  Catriel Beeri,et al.  A Sophisticate's Introduction to Database Normalization Theory , 1978, VLDB.

[6]  Moshe Y. Vardi.  On decomposition of relational databases , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[7]  Catriel Beeri,et al.  On the Properties of Join Dependencies , 1979, Advances in Data Base Theory.

[8]  Joachim Biskup,et al.  Synthesizing independent database schemas , 1979, SIGMOD '79.

[9]  Alfred V. Aho,et al.  The theory of joins in relational data bases , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[10]  Jeffrey D. Ullman,et al.  Principles of Database Systems , 1980 .

[11]  Philip A. Bernstein,et al.  Computational problems related to the design of normal form relational schemas , 1979, TODS.

[12]  Catriel Beeri,et al.  A Proof Procedure for Data Dependencies , 1984, JACM.

[13]  David Maier,et al.  Adequacy of Decompositions of Relational Databases , 1980, J. Comput. Syst. Sci..