R. J. Daigle Normalization Concepts CIS 507 Database Programming

R. J. Daigle Two types of Anomalies associated with databases. Modification Anomaly –an unexpected consequence of changing the actual data in a database Design Anomaly –a flaw in the logical design of the database itself Basic Principles: –For each modification anomaly there is a design anomaly –For each design anomaly there are associated modification anomalies Introduction EmployeeIDLast NameFirst Name JonesSamual SmithSandra EdwardsEdwin EmployeeID

R. J. Daigle Types of modification anomalies: Insertion: –add a new student—since the key is STUDENT-ID + COURSE, a student can only be added when the course has been completed. Deletion: –of student results in the loss of information about course CIS 503. Update. –Student to Tonya Marshall requires the change to take place in several places. STUDENT-IDSTUDENT-NAMECOURSECOURSE NAMEGRADE John SmithCIS 501Accelerated ProgrammingB Tonya TuckerCIS 501Accelerated ProgrammingB Tonya TuckerCIS 502Architecture and OSA Michael BoydCIS 503Data and File StructureA George JonesCIS 502Architecture and OSB Tonya TuckerCIS 504Networks & CommunicationsC

R. J. Daigle Normalization Design anomalies have been classified and criteria for removal of the anomalies have been developed. The process of removing design anomalies is called Normalization. A Normal Form is associated with the removal of a specific type of anomaly. The known normal forms from lowest to highest are: 1NF, 2NF, 3NF, BCNF, 4NF, 5NF, DKNF Any design which is evaluated as a higher form automatically satisfies the lower forms.

R. J. Daigle Normalization Theory of Normalization Contributors –Dr. E. F. Codd introduced the first three normal forms in the same paper in which the Relational Model was introduced ( A Relational Model of Data for Large Shared Databanks, CACM, Vol 13, No 6, June, 1970.) –Dr. R. F. Boyce extended Codd's original three forms. –Dr. R. Fagin extended the theory as proposed by Codd and introduced another way of evaluating a design. –Dr. D. M. Kroenke has been instrumental in clarifying the theory of normal forms in his role as educator.

R. J. Daigle Known Normal Forms. The normal forms in order from lowest to highest are –First Normal Form (1NF). Elimination of repeating field types –Second Normal Form (2NF). Elimination of partial key dependencies. –Third Normal Form (3NF). Elimination of transitive key dependencies among non-key attributes. –Boyce-Codd Normal Form (BCNF). Elimination of partial key dependencies upon non-key attributes. –Fourth Normal Form (4NF). Elimination of multi-valued dependencies. –Fifth Normal Form (5NF). Elimination of join anomalies. –Domain Key Normal Form. Elimination of all modification anomalies.

R. J. Daigle Basic Definitions. Assumptions: –e is an entity type –ε is the set of attributes for e –A, B, C,... are non-empty subsets of ε

R. J. Daigle Basic Definitions. Functional Dependence: B is Functionally Dependent on A if for each value of A there is exactly one value of B. –A is said to Functionally Determine B –A is called a Determinant. –The relationship between A and B is represented as A --> B –If A --> ε, A is said to be an Identifier for the entity type e Example e = STUDENT-DORM-FEE ε = {STUD-ID, STUD-NAME, DORM, DORM-FEE} A = {STUD-ID} B = {DORM} C = {DORM-FEE} A --> ε, B --> C

R. J. Daigle Key K is a Key for the entity e if and only if 1.K --> ε and 2.no non-empty subset of K determines ε. Example (From last example) –A = {STUD-ID} is a key for e = STUDENT-DORM- FEE –{STUD-ID, DORM-FEE} is not a key for e. An attribute which belongs to the selected key A is called a Key Attribute; all other attributes are called Non-Key Attributes.

R. J. Daigle First Normal Form (1NF) (Repeating Attribute Types) A is a repeating attribute type or repeating field type if for each occurrence of e there may be 0, 1, or more occurrences of values for A. The data structure used for a repeating attribute types gives rise to maintenance difficulties. –Static approach: embedding repeating field type is within the entity type (implemented as an array) allocation for maximal perceived use results in unused space or insufficient storage for some entities if the maximal perceived use is underestimated –Dynamic approach: data structure which requires more complex functions for management. Example. –e = {STUD-ID, STUD-NAME, COURSE, COURSE-GRADE} COURSE and COURSE-GRADE form a repeating type pair of attributes since any student will have completed 0, 1, or more courses.

R. J. Daigle First Normal Form (1NF) (Atomic Attributes) An attribute is Atomic if the attribute defines the lowest level of usage of data collected for the attribute. Example. e = {STUD-ID, STUD-NAME, COURSE, COURSE-GRADE} –No guarantee that LAST-NAME will available since the design does not define it as an attribute. –Examples for Johnson Albert Gilbert: JOHNSON GILBERT, GILBERT JOHNSON, J. A. GILBERT, J. GILBERT, GILBERT J., GILBERT J. A., JOHNSON A. GILBERT, J. ALBERT GILBERT, GILBERT JOHNSON A., GILBERT JOHNSON ALBERT, JOHNSON ALBERT GILBERT, GILBERT J. ALBERT, etc. –The forms shown above might all be present for different entities in the data collection. –Any algorithm designed to extract the desired information would have to consider all possibilities. –Avoided by properly identifying the lowest level of use during the design phase rather than relying on an application to obtain the desired data.

R. J. Daigle First Normal Form (1NF) (Definition) An entity type e is in FIRST NORMAL FORM (1NF) if and only if 1.e has no repeating attribute types AND 2.all attribute types of e are atomic.

R. J. Daigle Token Diagram (Abstraction). A B C D 1 D 2 E

R. J. Daigle Symbolic Table. Insertion Anomaly. b.Deletion Anomaly. c.Update Anomaly. ABCDGRADE John SmithCIS 501Accelerated ProgrammingB Tonya TuckerCIS 501Accelerated ProgrammingB Tonya TuckerCIS 502Architecture and OSA Michael BoydCIS 503Data and File StructureA George JonesCIS 502Architecture and OSB Tonya TuckerCIS 504Networks & CommunicationsC

R. J. Daigle Second Normal Form (Partial Key Dependency) An entity type e with key, K, has a Partial Key Dependency if and only if a collection of non-key attributes is determined by (or functionally dependent on) a non-empty proper subset of K.

R. J. Daigle Second Normal Form (Definition) An entity type e is in SECOND NORMAL FORM (2NF) if and only if a.e is in 1NF AND b.e has no partial key dependencies.

R. J. Daigle Example. Difficulties. A B C D

R. J. Daigle Token Diagram (Abstraction). A B C D A B C D A

R. J. Daigle Symbolic Table. a.Insertion Anomaly. b.Deletion Anomaly. c.Update Anomaly.

R. J. Daigle Third Normal Form (3NF). For A and C, attribute collections for an entity type e, there is a Transitive Dependency of C upon A if there is an attribute collection, B, of e for which a.A --> B and b.B --> C.

R. J. Daigle Third Normal Form (Definition) An entity type e is in THIRD NORMAL FORM (3NF) if and only if a.e is in 2NF AND b.e has no transitive dependencies of one non-key attribute collection upon another non-key attribute collection

R. J. Daigle Example Difficulties.

R. J. Daigle Token Diagram (Abstraction)

R. J. Daigle Symbolic Table. Insertion Anomaly. Deletion Anomaly. Update Anomaly.

R. J. Daigle Boyce-Codd Normal Form (BCNF). Attribute collections A and B of an entity type e are Candidate Keys for e if and only if a.A is a key for e and b.B is a key for e and c.A is not equal to B.

R. J. Daigle Boyce-Codd Normal Form (BCNF) (Definition) An entity type e is in BOYCE-CODD NORMAL FORM (BCNF) if and only if a.e is in 3NF AND b.all determinants of e are candidate keys.

R. J. Daigle Example. Difficulties.

R. J. Daigle T oken Diagram (Abstraction) Second Normal Form (Partial Key Dependency)

R. J. Daigle Symbolic Table. a.Insertion Anomaly. b.Deletion Anomaly. c.Update Anomaly.