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More about Functional Dependencies and Normalization

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Functional Dependencies A functional dependency occurs when the value of one (set of) attribute(s) determines the value of a second (set of) attribute(s) –X Y if, and only if, whenever two rows agree on X, they must necessarily agree on Y The attribute on the left side of the functional dependency is called the determinant –SID DormName, Fee –(CustomerNumber, ItemNumber, Quantity) Price While a primary key is always a determinant, a determinant is not necessarily a primary key Functional dependencies are fundamental to database “normalization”

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Functional Dependencies EmpName,SSN,BirthDate,Address,DeptNo,DeptName (This is not a well designed schema, as we will see…) While a primary key is always a determinant, a determinant is not necessarily a primary key. Here SSN is the primary key, and it is also true that within each row, DeptNo determines DeptName.

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Normalization Normalization eliminates modification anomalies –Deletion anomaly: deletion of a row loses information about two or more entities –Insertion anomaly: insertion of a fact in one entity cannot be done until a fact about another entity is added Anomalies can be removed by splitting the relation into two or more relations; each with a different, single theme However, breaking up a relation may create referential integrity constraints Normalization works through classes of relations called normal forms

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Relation schemas suffering from update anomalies: EmpName,SSN,BirthDate,Address,DeptNo,DeptName ProjectNo,SSN,Hours,EmpName,ProjName,ProjLocation Why so?

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Normal Forms Any table of data is in 1NF if it meets the definition of a relation A relation is in 2NF if all its non-key attributes are dependent on all of the key (no partial dependencies) –If a relation has a single attribute key, it is automatically in 2NF A relation is in 3NF if it is in 2NF and has no transitive dependencies A relation is in BCNF if every determinant is a candidate key A relation is in 4NF if it is in BCNF and has no multi- value dependencies

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2 nd Normal Form ProjectNo|SSN|Hours|EmpName|ProjName|ProjLocation Employee_Project relation ProjectNo|SSN|HoursSSN|EmpName ProjectNo|ProjName|ProjLocation So, in 2 nd Normal Form becomes 3 relations: EmployeeProject_Hours Project A relation is in 2NF if all its non-key attributes are dependent on all of the key.

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Third Normal Form: EmpName,SSN,BirthDate,Address,DeptNo,DeptName A relation is in 3NF if it is in 2NF and has no transitive dependencies. So, in 3NF becomes two relations: EmpName,SSN,BirthDate,Address,DeptNo DeptNo,DeptName

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Another BCNF example: Every determinant must be a candidate key StudentID | Course | Instructor Coursework relation in 3NF: Student | InstructorInstructor | Course In BCNF becomes 2 relations: Instructor-Course:Student-Course: Nora JonesDatabaseReynolds Willie NelsonPLCVanWie Willie NelsonOperating SystemsCarithers Jane ManheitDatabaseReynolds

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A 4NF example: EmployeeName,ProjectName,DependentName Nora JonesSwingTimenone Willie Nelson OnTheRoad ProblemsWithIRS Sam Lisa Willie Nelson ProblemsWithIRS OnTheRoad Sam Lisa Jane Manheit Standards Linda Bill EmployeeName,DependentName EmployeeName,ProjectName In 4NF becomes 2 relations: Employee-Project: Employee-Dependent:

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De-normalized Designs When a normalized design is unnatural, awkward, or results in unacceptable performance, a de- normalized design is preferred Example –Normalized relation CUSTOMER (CustNumber, CustName, Zip) CODES (Zip, City, State) –De-Normalized relations CUSTOMER (CustNumber, CustName, City, State, Zip)

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