Functional Dependencies Database Development • Requirements Analysis • Collect and Analyze the requirements of the users. • Conceptual Design • Design a conceptual model, e.g., ER model. • Logical Design • Translate the ER model into the relational model. • Normalization. • Database Building (Physical Design) • Build the database and write application programs. • Operation, Maintenance, & Tuning • Use, maintain, and “tune” the database. 2 Normalization • Decides which attributes should be grouped together in a relation • Validates and improves the logical proceeding to physical design. design to the point before • Based on the concept of Functional dependency. 3 Normalization • Normalization • To ensure you have a “good” design. • To prove you have got a “good” one. • To rescue a “bad” one. • How? • Decompose a “bad” table into several “good” ones. • Move from a lower normal form to a higher (better) one. • But what’s a “good” design? 4 Good Database Design • • no redundancy of FACT (!) no inconsistency examples: M/F or 1/0, Ahmed or Ahmad etc., this creates anomalies Anomalies: Abnormal, Deviation from common rule • • • no insertion, deletion or update anomalies no information loss no dependency loss 5 Data Redundancy • Major aim of relational database design is to group attributes into relations to minimize data redundancy and reduce file storage space required by base relations. • Problems associated with data redundancy are illustrated by comparing the following Staff and Branch relations with the StaffBranch relation. 6 Data Redundancy: Example-1 • StaffBranch relation has redundant data: details of a branch are repeated for every member of staff. Dr. Ejaz Ahmed 7 Redundancy leads to anomalies StudentDepartment Student Department StudentDepartment Could we insert a department without a student? We cannot insert a department who has no students, as studentID will have a NULL value, which is not allowed as studentID is the primary key. Insert Anomaly • The inability to insert valid data into database due to absence of certain another data is called insertion anomaly. • To update a value, we need to update multiple rows. • After update, same object has different values which leads to inconsistency Update anomaly • When redundant data is updated, data inconsistency may occur due to partial update of data. Can we keep student 3 and delete student information ? We cannot delete student 3 without loosing department information as student 3 is the only student of that department Delete anomaly • A delete anomaly occurs when deletion of some information leads to loss of some another valid data SOLUTION • These anomalies are addressed by Normalization. • The normalization makes sure that all these three issues and other possible be addressed at the time of designing. • Based on the concept of Functional dependency. Functional Dependency • The attributes of a table is said to be dependent on each other when an attribute of a table uniquely identifies another attribute of the same table. • It defines a relationship between two attributes, typically between the PK and other non-key attributes within a table. • Functional Dependency helps to maintain the quality of data in the database. • It plays a vital role to find the difference between good and bad database design. RollNo FirstName RollNo LastName RollNo Marks FirstName RollNo LastName RollNo Marks RollNo Functional Dependency • Let R be a table, • and let X and Y be sets of attributes of R (X is on LHS and Y is on RHS of an arrow pointing from left to right), • if the value of X always uniquely determines the value of Y. then Y is functionally dependent (FD) on X, • We write: X --> Y (read “X functionally determines Y”, or “X arrows to Y”) Or Y is associated with X • X is called the determinant. Y is the dependent. X Y Y is functionally dependent on X / X functionally determines Y (All attributes) of X uniquely determines Y (All attributes) SSN Movie (title, year, length, filmType, studioName, starName). title, year length title, year filmType title, year studioName shorthand: title year length,filmType, studioName Functional Dependencies • Functional dependencies (FDs) are used to specify formal measures of the "goodness" of relational designs • FDs and keys are used to define normal forms for relations • FDs are constraints that are derived from the meaning and inter-relationships of the data attributes Types of Functional Dependencies • Fully functionally dependent • Partially functionally dependent • Trivial functional Dependence • Non-Trivial functional Dependence • Completely Non-Trivial functional Dependence • Transitive Dependency Example_01: Fully Functionally Dependent ItemPrice SupplierID, ItemID Price SupplierID Price ItemPrice SupplierID Price ItemPrice ItemID Price ItemPrice SupplierID, ItemID Price SupplierID Price ItemID Price Fully Functionally dependent Fully functionally dependent • If X and Y are attribute set of a relation, Y is fully functionally dependent on X if Y is functionally dependent on X, but not on any proper subset of X Example_02: Partially Functionally Dependent StudentID, DeptID DeptName DeptID DeptName Partial Functionally dependent Partial functionally dependent • A functional dependency X Y is a partial dependency if there is some attribute that can be removed from X and yet the dependency still holds. FD1: StudentID, CourseID StudentName FD2: CourseID CourseName FD3: StudentID, CourseID CourseName FD4: CourseID CourseName FD5: StudentID, CourseID Grade StudentID Grade CourseID Grade Partial Functionally dependent Full Functionally dependent Partial Functionally dependent Full Functionally dependent Full Functionally dependent Trivial Functional Dependency • The functional dependency XY is a trivial functional dependency if Y is subset of X. StudentID, StudentName StudentID StudentID StudentID Non-Trivial Functional Dependency The functional dependency XY is a non-trivial functional dependency if Y is not a subset of X. StudentID Branch StudentID, StudentName Branch StudentID, StudentName StudentName , Branch Completely Non-Trivial Functional Dependency • The functional dependency XY is completely non-trivial functional dependency if X intersection Y is null. StudentID Branch StudentID, StudentName Branch StudentID, StudentName StudentName , Branch Non-trivial Transitive Functional Dependency A transitive dependency in a database is an indirect relationship between values in the same table that causes a functional dependency. • Let X,Y,Z be attributes of a relation R, • If X Y and YZ, then Z is transitively dependent on X. FD1: StudentID DepID FD2: DepID DepName FD3: StudentID DepName Transitive Functional Dependency (Example) FD1: Book → Author FD2: Author → Author_Nationality FD3: Book →Author_Nationality:
