4N and the Normalization of Multivalue Dependency By: Laith Alnagem

Rules Fourth Normal Form - if R is 3N and BCNF… - given the “non-trivial” MVD: A 1 A 2 …A n  B 1 B 2 …B n {A 1 A 2 …A n } is a superkey A MVD: A 1 A 2 …A n  B 1 B 2 …B n for a Relation R is “non- trivial” if: 1.none of the Bs are among the As 2.Not all of the attributes of R are among the As and Bs A MVD is “trivial” if it contains all the variations of A 1 A 2 …A n x B 1 B 2 …B n. or α  ß is ß  α or ß  α

Formal Definition Let R be a relation schema and let α  R and ß  R. The multivalued dependency α  β holds on R if, in any legal relation r(R), for all pairs of tuples t1 and t2 in r such that t1[α] = t2[α], there exist tuples t3 and t4 in r such that t1[α] = t2[α] = t3[α] = t4[α] t3[β] = t1[β] t3[R − β] = t2[R − β] t4[β] = t2[β] t4[R − β] = t1[R − β][1][1]

Multivalued Dependency in 4N A table with a multivalued dependency is one where the existence of more than one independent many-to-many relationships in a table causes redundancy; and it is this redundancy which is removed by fourth normal form.

Example RestaurantPizza VarietyDelivery Area Elite PizzaThin CrustCapital City Elite PizzaStuffed CrustCapital City A1 PizzaThick CrustSpringfield A1 PizzaThick CrustShelbyville A1 PizzaThick CrustCapital City A1 PizzaStuffed CrustSpringfield A1 PizzaStuffed CrustShelbyville A1 PizzaStuffed CrustCapital City

Example (cont’) It is 1N, 2N, 3N and BCNF But because the varieties of pizza a restaurant offers are independent from the areas to which the restaurant delivers, there is redundancy in the table: for example, we are told three times that A1 Pizza offers Stuffed Crust, and if A1 Pizza start producing Cheese Crust pizzas then we will need to add multiple records, one for each of A1 Pizza's delivery areas.

The Fix RestaurantPizza VarietyDelivery Area Elite PizzaThin CrustCapital City Elite PizzaStuffed CrustCapital City A1 PizzaThick CrustSpringfield A1 PizzaThick CrustShelbyville A1 PizzaThick CrustCapital City A1 PizzaStuffed CrustSpringfield A1 PizzaStuffed CrustShelbyville A1 PizzaStuffed CrustCapital City

RestaurantPizza Variety Elite PizzaThin Crust Elite PizzaStuffed Crust A1 PizzaThick Crust A1 PizzaStuffed Crust RestaurantDelivery Area Elite PizzaCapital City A1 PizzaSpringfield A1 PizzaShelbyville A1 PizzaCapital City

A little thought Q: What if the pizza varieties offered by a restaurant sometimes did vary from one delivery area to another?

A: Then the original three-column table would satisfy 4NF

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Conclusions Databases with multivalued dependencies exhibit redundancy. In database normalization, fourth normal form requires that databases have no multivalued dependencies.database normalizationfourth normal form

Extra Transitivity, Reflexivity, Complementation, Replication, Augmentation and a few more are all properties of 4 th normal form

References Multivalued dependency From Wikipedia, the free encyclopedia Revision as of 11:59, 24 October 2006 by GurchBot (Talk | contribs) (diff) ← Older revision | Current revision | Newer revision → (diff)GurchBotTalkcontribsdiff← Older revision DataBase: System Concepts (5 th Edition) Ch-7 Silberschatz, Korth, Sudarshan NY, 2006