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4N and the Normalization ofMultivalue Dependency

By:

Laith Alnagem

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Rules

Fourth Normal Form- if Ris 3N and BCNF

- given the non-trivial MVD: A1A2An B1B2Bn{A1A2An} is a superkey

A MVD: A1A2An B1B2Bn for a Relation Ris non-trivial if:

1. none of the Bs are among the As2. Not all of the attributes of Rare among the As and Bs

A MVD is trivial if it contains all the variations ofA1A2AnxB1B2Bn.

or is or

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Formal Definition

Let Rbe a relation schema and let Rand R .The multivalued dependency

holds on R if, in any legal relation r(R), for all pairs oftuples t1 and t2 in rsuch that t1[] = t2[], there existtuples t3 and t4 in rsuch thatt1[] = t2[] = t3[] = t4[]t3[] = t1[]t3[R ] = t2[R ]t4[] = t2[]t4[R ] = t1[R ][1]

http://en.wikipedia.org/wiki/Multivalued_dependencyhttp://en.wikipedia.org/wiki/Multivalued_dependency

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Multivalued Dependency in 4N

A table with a multivalued dependency is one

where the existence of more than oneindependent many-to-many relationships in atable causes redundancy; and it is thisredundancy which is removed by fourth

normal form.

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Example

Restaurant Pizza Variety Delivery Area

Elite Pizza Thin Crust Capital City

Elite Pizza Stuffed Crust Capital City

A1 Pizza Thick Crust Springfield

A1 Pizza Thick Crust Shelbyville

A1 Pizza Thick Crust Capital City

A1 Pizza Stuffed Crust Springfield

A1 Pizza Stuffed Crust Shelbyville

A1 Pizza Stuffed Crust Capital City

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Example (cont)

It is 1N, 2N, 3N and BCNF

But because the varieties of pizza a restaurant offersare independent from the areas to which therestaurant delivers, there is redundancy in the table:

for example, we are told three times that A1 Pizzaoffers Stuffed Crust, and if A1 Pizza start producing

Cheese Crust pizzas then we will need to addmultiple records, one for each of A1 Pizza's deliveryareas.

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The Fix

Restaurant Pizza Variety Delivery Area

Elite Pizza Thin Crust Capital CityElite Pizza Stuffed Crust Capital City

A1 Pizza Thick Crust Springfield

A1 Pizza Thick Crust Shelbyville

A1 Pizza Thick Crust Capital City

A1 Pizza Stuffed Crust Springfield

A1 Pizza Stuffed Crust Shelbyville

A1 Pizza Stuffed Crust Capital City

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Restaurant Pizza Variety

Elite Pizza Thin Crust

Elite Pizza Stuffed Crust

A1 Pizza Thick Crust

A1 Pizza Stuffed Crust

Restaurant Delivery Area

Elite Pizza Capital City

A1 Pizza Springfield

A1 Pizza Shelbyville

A1 Pizza Capital City

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A little thought

Q:

What if the pizza varieties offered by arestaurant sometimes did vary from onedelivery area to another?

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A:

Then the original three-column table wouldsatisfy 4NF

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Course Book Lecturer

AHA Silberschatz John D

AHA Nederpelt John D

AHA Silberschatz William M

AHA Nederpelt William M

AHA Silberschatz Christian G

AHA Nederpelt Christian G

OSO Silberschatz John D

OSO Silberschatz William M

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A.

1. {course} {book}2. {course} {lecturer}

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Conclusions

Databases with multivalued dependencies

exhibit redundancy. In database normalization, fourth normal

form requires that databases have nomultivalued dependencies.

http://en.wikipedia.org/wiki/Database_normalizationhttp://en.wikipedia.org/wiki/Fourth_normal_formhttp://en.wikipedia.org/wiki/Fourth_normal_formhttp://en.wikipedia.org/wiki/Fourth_normal_formhttp://en.wikipedia.org/wiki/Fourth_normal_formhttp://en.wikipedia.org/wiki/Database_normalization

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Extra

Transitivity, Reflexivity, Complementation,

Replication, Augmentation and a few moreare all properties of 4th normal form

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References

Multivalued dependency

From Wikipedia, the free encyclopedia

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DataBase: System Concepts (5th Edition) Ch-7

Silberschatz, Korth, Sudarshan

NY, 2006

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