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A '''canonical cover''' <math>F_c</math> for F (a set of [[Functional dependency|functional dependencies]] on a [[Relation (database)|relation scheme]]) is a set of dependencies such that F logically implies all dependencies in <math>F_c</math>, and <math>F_c</math> logically implies all dependencies in F.  
 
The set <math>F_c</math> has two important properties:
 
# No functional dependency in <math>F_c</math> contains an extraneous attribute.
# Each left side of a functional dependency in <math>F_c</math> is unique. That is, there are no two dependencies <math>a \to b</math> and <math>c \to d</math> in <math>F_c</math> such that <math>a = c</math>.
 
== Algorithm for computing a canonical cover <ref>''Database system concepts'' by Abraham Silberschatz et al</ref>==
 
# <math>F_c = F</math>
# Repeat:
## Use the union rule to replace any dependencies in <math>F_c</math> of the form <math>a \to b</math> and <math>a \to d</math> with <math>a \to bd</math>.
## Find a functional dependency in <math>F_c</math> with an extraneous attribute and delete it from <math>F_c</math>
# ... until <math>F_c</math> does not change
 
== References ==
{{reflist}}
 
[[Category:Database theory]]
[[Category:Mathematical concepts]]
[[Category:Algorithms and data structures]]

Revision as of 00:26, 16 January 2014

A canonical cover Fc for F (a set of functional dependencies on a relation scheme) is a set of dependencies such that F logically implies all dependencies in Fc, and Fc logically implies all dependencies in F.

The set Fc has two important properties:

  1. No functional dependency in Fc contains an extraneous attribute.
  2. Each left side of a functional dependency in Fc is unique. That is, there are no two dependencies ab and cd in Fc such that a=c.

Algorithm for computing a canonical cover [1]

  1. Fc=F
  2. Repeat:
    1. Use the union rule to replace any dependencies in Fc of the form ab and ad with abd.
    2. Find a functional dependency in Fc with an extraneous attribute and delete it from Fc
  3. ... until Fc does not change

References

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  1. Database system concepts by Abraham Silberschatz et al