An introduction to database systems: vol. I (4th ed.)
An introduction to database systems: vol. I (4th ed.)
Synthesizing third normal form relations from functional dependencies
ACM Transactions on Database Systems (TODS)
A relational model of data for large shared data banks
Communications of the ACM
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Normalization and functional dependencies in the relational data base model.
Normalization and functional dependencies in the relational data base model.
An improved third normal form for relational databases
ACM Transactions on Database Systems (TODS)
A hierarchical method for synthesizing relations
ACM-SE 20 Proceedings of the 20th annual Southeast regional conference
On the merge of factor canonical bases
ICFCA'08 Proceedings of the 6th international conference on Formal concept analysis
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Numerous algorithms concerning relational databases use a cover for a set of functional dependencies as all or part of their input. Examples are Bernstein and Beeri's synthesis algorithm [BB] and the tableau modification algorithm of Aho, Beeri, and Ullman [ABU]. The performance of these algorithms may depend both on the number of functional dependencies in the cover and the total size of the cover. Starting with a smaller cover will make such algorithms run faster. After Bernstein [Be75], many researchers believe the problem of finding a minimum cover is NP-complete. We show that minimum covers can be found in polynomial time, using the notion of direct determination. The proof details the structure of minimum covers, refining the structure Bernstein and Beeri show for non-redundant covers [BB]. The kernel algorithm of Lewis, Sekino, and Ting [LST] is improved using these results.