lec10.366 - . . Winter 2008 CPE/CSC 366: Database Modeling,...

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. . Winter 2008 CPE/CSC 366: Database Modeling, Design and Implementation Alexander Dekhtyar . . Theory of Normal Forms Decomposition of Relations Overview Functional Dependencies capture the attribute dependencies within a rela- tional table. Functional Dependencies that do not involve full keys lead to anomalies : problems with management/maintenance of tables. Normal Forms are restrictions on functional dependencies in relational ta- bles. Third Normal Form (3NF) and Boyce-Codd Normal Form (BCNF eliminate from relational tables FDs that do not involve full keys 1 . If a table in a database schema violates 3NF, often it is best to replace it with a collection of tables in 3NF. This is achieved via the procedure called decomposition of relations . Relational table decomposition: replacement of a relational table R ( A 1 ,...,A n ) with relational tables R 1 , R 2 ,...,R k . We want relational decomopositions to have the following properties: P1. For all i , R i = π L ( R ), where L ⊂ { A 1 ,...,A n } . P2. R 1 ⊲⊳ R 2 ⊲⊳ . ..R k = R . Decompositions are designed to address the following issues: Eliination of anomalies . Property P1 usually takes care of that. Recoverability of information . This is achieved by decompositions satisfying property P2 . Preservation of dependencies . This is an important challenge. It may a±ect how far towards normalization we can get. 1 Remember, in case of 3NF, it is possible to have an FD involving an incomplete key, but the right side of such FD hase to be a prime attribute. 1
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Algorithms for Functional Dependencies In order to present the algorithm for decomposing any relation into a relational schema in 3NF, we ±rst need two algorithms involving functional dependencies: Closure : given a list of attributes and a set of FDs ±nd all attributes that depend on it.
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This note was uploaded on 05/19/2008 for the course CSC 365 taught by Professor Dekhtyar during the Spring '08 term at Cal Poly.

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lec10.366 - . . Winter 2008 CPE/CSC 366: Database Modeling,...

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