BCNF Decomposition: Difference between revisions

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== Problem Description==
{{DISPLAYTITLE:BCNF Decomposition (BCNF Decomposition)}}
== Description ==  


BCNF Decomposition is the problem of decomposing a relation schema into Boyce-Codd normal form (BCNF).


== Bounds Chart ==
A relation schema $R$ is in Boyce Codd Normal Form (abbr. BCNF) if for all non-trivial FDs $X \rightarrow Y$ in $F^+$, $X$ is a superkey. In extending this notion to database schemas, we must be conscious of the UR-assumption. We say that $R_i = <ATTR_i,F_i>$ is in BCNF if the schema $<ATTR_i, F^+(ATTR_i)>$ is in BCNF, and $D$ is in BCNF if each $R_i$ is.
[[File:BCNF_DecompositionBoundsChart.png|350px]]


== Step Chart ==
== Related Problems ==  
[[File:BCNF_DecompositionStepChart.png|350px]]


== Improvement Table ==
Related: [[Decisional BCNF]]
{| class="wikitable" style="text-align:center;" width="100%"
 
!width="20%" | Complexity Classes !! width="40%" | Algorithm Paper Links !! width="40%" | Lower Bounds Paper Links
== Parameters ==  
|-
 
| rowspan="1" | Exp/Factorial
$n$: size of database?
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|
$k$: number of functional dependencies
|-
 
| rowspan="1" | Polynomial > 3
== Table of Algorithms ==
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|
Currently no algorithms in our database for the given problem.
|-
 
| rowspan="1" | Cubic
== Time Complexity Graph ==  
|
 
|
[[File:BCNF Decomposition - Time.png|1000px]]
|-
| rowspan="1" | Quadratic
|
|
|-
| rowspan="1" | nlogn
|
|
|-
| rowspan="1" | Linear
|
|
|-
| rowspan="1" | logn
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|-|}

Latest revision as of 10:09, 28 April 2023

Description

BCNF Decomposition is the problem of decomposing a relation schema into Boyce-Codd normal form (BCNF).

A relation schema $R$ is in Boyce Codd Normal Form (abbr. BCNF) if for all non-trivial FDs $X \rightarrow Y$ in $F^+$, $X$ is a superkey. In extending this notion to database schemas, we must be conscious of the UR-assumption. We say that $R_i = <ATTR_i,F_i>$ is in BCNF if the schema $<ATTR_i, F^+(ATTR_i)>$ is in BCNF, and $D$ is in BCNF if each $R_i$ is.

Related Problems

Related: Decisional BCNF

Parameters

$n$: size of database?

$k$: number of functional dependencies

Table of Algorithms

Currently no algorithms in our database for the given problem.

Time Complexity Graph

BCNF Decomposition - Time.png