Normalization of DatabaseLecture - ANS

Yong Choi

School of Business

CSUB

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1NF Example

Unnormalized TablePK

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1NF Example (con’t.)

Conversion to 1NFPK

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Another 1NF Example

Cust_ID Name Street Phone

104 Mr. Ray Suchecki

123 Pond Hill Road, Detroit, MI, 48161

(313) 792-3546

Cust_ID SalesRep_Name Rep_Office Order_1 Order_2 Order_3

1022 Jones 412 10 14 19

PK

PK

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2NF ExamplePK PK

Each arrow shows partial dependency

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2NF Example

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Example of 3NF

PK: Cust_ID

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Relation with transitive dependency

PK

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Transitive dependency

• All attributes are functionally dependent on Cust_ID. – Cust_ID -> Name– Cust_ID -> Salesperson– Cust_ID -> Region

• However, there is a transitive dependency.– Region is functionally dependent on Salesperson.– Salesperson -> Region

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Problems with Transitive dependency

• A new sales person (Yong) assigned to the North region cannot be entered until a customer has been assigned to that salesperson (since a value for Cust_ID must be provided to insert a row in the relation).

• If customer number 6837 is deleted from the table, we lose the information that salesperson Hernandez is assigned top the Easy region.

• If sales person Smith is reassigned to the East region, several rows must be changed to reflect that fact.

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Decomposing the SALES relation

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Relations in 3NF

Now, there are no transitive dependencies…Both relations are in 3rd NF

CustID Name

CustID Salesperson

Salesperson Region

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Dependency Diagram

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Boyce-Codd Normal Form (BCNF)

• Special case of 3NF.• A relation is in BCNF if it’s in 3NF and there is no

hidden dependencies. • Below is in 3NF but not in BCNF

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BCNF

Stu_ID Advisor Major GPA

123 Nasa Physics 4.0

123 Elvis Music 3.3

456 King Literature 3.2

789 Jackson Music 3.7

678 Nasa Physics 3.5

Student

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BCNF

Stu_ID Advisor Major GPA

Don’t confuse with Transitive Dependency!

Advisor is functionally dependent on Major.

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BCNF

• In Physics the advisor Nasa is replaced by Einstein. This change must be made in two ( or more) rows in the table.

• If we want to insert a row with the information that Choi advises in MIS. This cannot be done until at least one student majoring in MIS is assigned Choi as an advisor.

• If student number 789 withdraw from school, we lose the information that Jackson advises in Music.

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Conversion to BCNF

Stu_ID Advisor GPA

123 Nasa 4.0

123 Elvis 3.3

456 King 3.2

789 Jackson 3.7

678 Nasa 3.5

Advisor Major

Nasa Physics

Elvis Music

King Literature

Jackson Music

Student Advisor

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Decomposition into BCNF

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3NF and BCNF

• In practice, most relation schemas that are in 3NF are also in BCNF. Only if a hidden dependency X -> A exists in a relation.

• In general, it is best to have relation schemas in BCNF. If that is not possible, 3NF will do. However, 2NF and 1NF are not considered good relation schema designs.

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4NF

• A relation is in 4NF if it is already in 3NF and does not contain two multi-valued dependencies that are independent.- it’s a different meaning than not having multi-valued attributes for 1NF.

e.g.,

Smith can cook and type.

Smith speaks French, German, and Greek

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4NF

E_Name Skill Language

Smith cook null

Smith type null

Smith null French

Smith null German

Smith null Chinese

E-Name ->-> SkillE-Name ->-> Language

PK

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4NF

The values for Skill and the values for Language are independent.

E_Name Skill E_Name Language

Smith Cook Smith French

Smith Type Smith German

Smith Chinese

PK PK

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Faculty (A) relation

FacultyNum StudentNum CommitteeCode

123 12805

24139

ADV

HSG

PER

444 57384 HSG

456 24139

36273

37573

CUR

Faculty (A) – normalized table

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Faculty (A) relation

• Each FacultyNum has a well-defined set of StudentNums.

• Each FacultyNum has a well-defined set of CommitteeCodeses.

• The STUDENTNUM and the COMMITTEECODE are independent of each other.

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Faculty (B) relationFaculty (B)

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Faculty (B) relation

• Has a composite PK– FacultyNum, StudentNum , and CommitteeCode

• Since there are no determinants other than the PKs, the relation is in BCNF.

• Yet it does contain much redundant data that can easily lead to update anomalies because of multi-valued dependencies.

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Problems with Faculty (B) relation

• Changing the CommitteeCode for faculty member requires more than one change.

• Suppose that a new faculty member 555 but does not yet serve on any committee. When a facultyNum 555 begins advising student 44332, there is a problem because the CommitteeCode is a part of PK.

• If faculty member 444 no longer advises student 57384 and delete appropriate record from the relation, we lose the information that faculty member serves on the Housing committee (HSG).

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Conversion to 4NF