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In database design, a lossless join decomposition is a decomposition of a relation into relations , such that a natural join of the two smaller relations yields back the original relation. This is central in removing redundancy safely from databases while preserving the original data. [ 1 ]
Database normalization is the process of structuring a relational database accordance with a series of so-called normal forms in order to reduce data redundancy and improve data integrity.
The join dependency plays an important role in the fifth normal form (5NF), also known as project-join normal form, because it can be proven that if a scheme is decomposed in tables to , the decomposition will be a lossless-join decomposition if the legal relations on are restricted to a join dependency on called (,, …,).
If a relational schema is in BCNF, then all redundancy based on functional dependency has been removed, [4] although other types of redundancy may still exist. A relational schema R is in Boyce–Codd normal form if and only if for every one of its functional dependencies X → Y, at least one of the following conditions hold: [5]
Given a set of functional dependencies , an Armstrong relation is a relation which satisfies all the functional dependencies in the closure + and only those dependencies. . Unfortunately, the minimum-size Armstrong relation for a given set of dependencies can have a size which is an exponential function of the number of attributes in the dependencies conside
Decomposition of 1NF into 2NF [ edit ] To make a 1NF relation a 2NF relation, remove the functionally dependent attributes in the partial dependencies of the first normal form relation, and place those partial dependency dependent attributes in a relation where their corresponding determinant attributes are an entire candidate key.
The third normal form (3NF) is a normal form used in database normalization. 3NF was originally defined by E. F. Codd in 1971. [2]Codd's definition states that a table is in 3NF if and only if both of the following conditions hold:
A decomposition of R into (X, Y) and (X, R − Y) is a lossless-join decomposition if and only if X Y holds in R. Every FD is an MVD because if X → {\displaystyle \rightarrow } Y, then swapping Y's between tuples that agree on X doesn't create new tuples.