Algorithmic Applications For A New Result On Multivalued Dependencies

Recently Delobel and Parker have shown that Multivalued dependencies (MVDs) may be represented as Boolean switching functions, in much the same way as Functional dependencies (FDs) can be represented as Boolean implications. This permits all FD and MVD inferences to be made as logical (Boolean) inferences, a significant plus because the FD/MVD inference axioms are fairly complex. This paper reviews some of the basic implications of this result and outlines new applications in FD/MVD membership testing, generation of dependency closure, cover, and keys, and testing for lossless and independent decompositions.

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

[2]  Jean-Marie Nicolas.  Mutual Dependencies and Some Results on Undecomposable Relations , 1978, VLDB.

[3]  János Demetrovics.  On the Number of Candidate Keys , 1978, Inf. Process. Lett..

[4]  Claude Delobel,et al.  Normalization and hierarchical dependencies in the relational data model , 1978, TODS.

[5]  Philip A. Bernstein,et al.  A unified approach to functional dependencies and relations , 1975, SIGMOD '75.

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

[7]  Ronald Fagin.  The Decomposition Versus Synthetic Approach to Relational Database Design , 1977, VLDB.

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

[9]  Alfred V. Aho,et al.  The Theory of Joins in Relational Data Bases (Extended Abstract) , 1977, FOCS.

[10]  FaginRonald.  Multivalued dependencies and a new normal form for relational databases , 1977 .

[11]  Philip A. Bernstein,et al.  Comment on "Decomposition of a Data Base and the Theory of Boolean Switching Functions" , 1977, IBM J. Res. Dev..

[12]  Curts,et al.  Adjacency Table Method of Deriving Minimal Sums , 1977, IEEE Transactions on Computers.

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

[14]  Carlo Zaniolo,et al.  Analysis and design of relational schemata for database systems. , 1976 .

[15]  Alberto O. Mendelzon.  On Axiomatizing Multivalued Dependencies in Relational Databases , 1979, JACM.

[16]  Charles R. Kime,et al.  An Efficient Algorithm for Finding an Irredundant Set Cover , 1974, JACM.

[17]  Daniel L. Ostapko,et al.  MINI: A Heuristic Approach for Logic Minimization , 1974, IBM J. Res. Dev..

[18]  Philip A. Bernstein,et al.  Synthesizing third normal form relations from functional dependencies , 1976, TODS.

[19]  Udo W. Pooch,et al.  A New Technique for the Fast Minimization of Switching Functions , 1977, IEEE Transactions on Computers.

[20]  Ronald Fagin,et al.  Functional Dependencies in a Relational Data Base and Propositional Logic , 1977, IBM J. Res. Dev..

[21]  Bernie L. Hulme,et al.  A Prime Implicant Algorithm with Factoring , 1975, IEEE Transactions on Computers.

[22]  Ronald Fagin,et al.  Multivalued dependencies and a new normal form for relational databases , 1977, TODS.

[23]  Catriel Beeri,et al.  A complete axiomatization for functional and multivalued dependencies in database relations , 1977, SIGMOD '77.