**NORMALIZATION
** The design database is required, so that we can have a database of compact and efficient in the use of storage space, quick and easy in the initialization manipulation (add, change, delete) data.

Database design process

Database design process

Gather user needs / business, Develop a needs-based ER Model user / business, Convert E-R model to the set of relations (tables) normalize relations, to remove anomalies, Implemented to create a database with a table for each relationship that is normalize

**DATABASE NORMALIZATION **

Normalization process is the establishment of the database structure so that most of the ambiguity can be removed. The process of normalization is the process of grouping data elements into a table-table and show relationship entity. In the process of normalization is always tested in some cases, if there are difficulties at the time to add / insert, delete / delete, change / update, and read / retrieve on a Database

Normalization stage, starting from the most mild (1NF) to most stringent (5NF) usually only reach the level of 3NF or BCNF because already sufficient to generate the table-a table of good quality.

Normalization must be done because:

- · Optimization table structures
- · Increase the speed
- · Eliminate income data the same
- · More efficient use of storage media
- · Reduce redundancy
- · Avoiding anomalies (insertion anomalies, deletion anomalies, update anomalies).
- · Improved data integrity

A table saying good (efficient) or if the normal 3 to meet the following criteria:

- · If there is decomposition (decomposition) table, it must be guaranteed safe decomposition (Lossless-Join Decomposition). That is, after the table is described a new table-table, the table-table can generate a new table with the same exact.
- · Maintain the functional dependence on the change data (Dependency preservation).
- · Not violate Boyce-Code Normal Form (BCNF)

If the three criteria (BCNF) can not be met, then at least the table does not violate the Normal Form of the third stage (3rd Normal Form / 3NF).

**FUNCTIONAL DEPENDENCY **

Functional Dependency describes a relationship attributes in relation

An attribute said functionally dependant on the other, if we use the value attribute to determine the value of the other attributes.

Are used to specify *formal measures* of the “goodness” of relational designs And keys are used to define **normal forms** for relations, Are **constraints** that are derived from the *meaning* and *interrelationships* of the data attributes. A set of attributes X *functionally* *determines* a set of attributes Y if the value of X determines a unique value for Y. X -> Y holds if whenever two tuples have the same value for X, they *must have *the same value for Y, For any two tuples t1 and t2 in any relation instance r(R): If t1[X]=t2[X], *then* t1[Y]=t2[Y]. X -> Y in R specifies a *constraint* on all relation instances r(R), Written as X -> Y; can be displayed graphically on a relation schema as in Figures. (Denoted by the arrow 🙂 FDs are derived from the real-world constraints on the attributes

Examples of FD constraints

- · Social security number determines employee name

o SSN -> ENAME

- · Project number determines project name and location

o PNUMBER -> {PNAME, PLOCATION}

- · Employee ssn and project number determines the hours per week that the employee works on the project {SSN, PNUMBER} -> HOURS

- · An FD is a property of the attributes in the schema R
- · The constraint must hold on
*every*relation instance r(R) - · If K is a key of R, then K functionally determines all attributes in R

o (since we never have two distinct tuples with t1[K]=t2[K])

FD’s are a property of the meaning of data and hold at all times: certain FD’s can be ruled out based on a given state of the database

** **

**Inference Rules for FDs**

- · Given a set of FDs F, we can
**infer**additional FDs that hold whenever the FDs in F hold

- · Armstrong’s inference rules:

o IR1. (**Reflexive**) If Y *subset-of* X, then X -> Y

o IR2. (**Augmentation**) If X -> Y, then XZ -> YZ

§ (Notation: XZ stands for X U Z)

o IR3. (**Transitive**) If X -> Y and Y -> Z, then X -> Z

- · IR1, IR2, IR3 form a
**sound**and**complete**set of inference rules

o These are rules hold and all other rules that hold can be deduced from these

- · Some additional inference rules that are useful:

o **Decomposition:** If X -> YZ, then X -> Y and X -> Z

o **Union:** If X -> Y and X -> Z, then X -> YZ

o **Psuedotransitivity:** If X -> Y and WY -> Z, then WX -> Z

- · The last three inference rules, as well as any other inference rules, can be deduced from IR1, IR2, and IR3 (completeness property)

- ·
**Closure**of a set F of FDs is the set F^{+}of all FDs that can be inferred from F - ·
**Closure**of a set of attributes X with respect to F is the set X^{+}of all attributes that are functionally determined by X - · X
^{+}can be calculated by repeatedly applying IR1, IR2, IR3 using the FDs in F

** **

**Equivalence of Sets of FDs**

- · Two sets of FDs F and G are
**equivalent**if:

o Every FD in F can be inferred from G, and

o Every FD in G can be inferred from F

o Hence, F and G are equivalent if F^{+} =G^{+}

- · Definition (
**Covers**):

o F **covers** G if every FD in G can be inferred from F

§ (i.e., if G^{+} *subset-of* F^{+})

- · F and G are equivalent if F covers G and G covers F

- · There is an algorithm for checking equivalence of sets of FDs

** **

**Minimal Sets of FDs**

- · A set of FDs is minimal if it satisfies the following conditions:

1. Every dependency in F has a single attribute for its RHS.

2. We cannot remove any dependency from F and have a set of dependencies that is equivalent to F.

3. We cannot replace any dependency X -> A in F with a dependency Y -> A, where Y proper-subset-of X ( Y subset-of X) and still have a set of dependencies that is equivalent to F.

- · Every set of FDs has an equivalent minimal set

- · There can be several equivalent minimal sets
- · There is no simple algorithm for computing a minimal set of FDs that is equivalent to a set F of FDs
- · To synthesize a set of relations, we assume that we start with a set of dependencies that is a minimal set

4. E.g., see algorithms 11.2 and 11.4

** **

**Computing the Minimal Sets of FDs**

We illustrate the above algorithm with the following:

Let the given set of FDs be *E *: {*B *→ *A*, *D *→ *A*, *AB *→ *D*}.We have to find the minimum cover of *E*.

- · All above dependencies are in canonical form; so we have completed step 1 of Algorithm 10.2 and can proceed to step 2. In step 2 we need to determine if
*AB*→*D*has any redundant attribute on the left-hand side; that is, can it be replaced by*B*→*D*or*A*→*D*? - · Since B → A, by augmenting with
*B*on both sides (IR2), we have*BB*→*AB*, or*B*→*AB*(i). However,*AB*→*D*as given (ii). - · Hence by the transitive rule (IR3), we get from (i) and (ii),
*B*→*D*. Hence*AB*→*D*may be replaced by*B*→*D*. - · We now have a set equivalent to original
*E*, say*E*′ : {*B*→*A*,*D*→*A*,*B*→*D*} No further reduction is possible in step 2 since all FDs have a single attribute on the left-hand side. - · In step 3 we look for a redundant FD in E′. By using the transitive rule on
*B*→*D*and*D*→*A*, we derive*B*→*A*. Hence*B*→*A*is redundant in E’ and can be eliminated. - · Hence the minimum cover of E is {
*B*→*D*,*D*→*A*}.

**Normalization of Relations**

- · Normalization:

o The process of decomposing unsatisfactory “bad” relations by breaking up their attributes into smaller relations

- · Normal form:

o Condition using keys and FDs of a relation to certify whether a relation schema is in a particular normal form

- · 2NF, 3NF, BCNF

o based on keys and FDs of a relation schema

- · 4NF

o based on keys, multi-valued dependencies : MVDs; 5NF based on keys, join dependencies : JDs (Chapter 11)

o Additional properties may be needed to ensure a good relational design

** **

**Practical Use of Normal Forms**

Normalization is carried out in practice so that the resulting designs are of high quality and meet the desirable properties The practical utility of these normal forms becomes questionable when the constraints on which they are based are *hard to understand* or to *detect, *The database designers *need not* normalize to the highest possible normal form

· (usually up to 3NF, BCNF or 4NF)

Denormalization is The process of storing the join of higher normal form relations as a base relation—which is in a lower normal form

** **

**Definitions of Keys and Attributes Participating in Keys**

A superkey of a relation schema R = {A1, A2, …., An} is a set of attributes S *subset-of* R with the property that no two tuples t1 and t2 in any legal relation state r of R will have t1[S] = t2[S], A key K is a superkey with the *additional property* that removal of any attribute from K will cause K not to be a superkey any more. If a relation schema has more than one key, each is called a candidate key.

- · One of the candidate keys is
*arbitrarily*designated to be the primary key, and the others are called secondary keys.

A Prime attribute must be a member of *some* candidate key, A Nonprime attribute is not a prime attribute—that is, it is not a member of any candidate key.

**First Normal Form (1NF)**

- · Disallows

o composite attributes

o multivalued attributes

o nested relations; attributes whose values for an *individual tuple* are non-atomic

- · Considered to be part of the definition of relation

**Normalization into 1NF**

**Normalization of nested relations into 1NF**

**Second Normal Form**

Uses the concepts of FDs, primary key

- · Definitions

o Prime attribute: An attribute that is member of the primary key K

o Full functional dependency: a FD Y -> Z where removal of any attribute from Y means the FD does not hold any more

- · Examples:

o {SSN, PNUMBER} -> HOURS is a full FD since neither SSN -> HOURS nor PNUMBER -> HOURS hold

o {SSN, PNUMBER} -> ENAME is not a full FD (it is called a partial dependency ) since SSN -> ENAME also holds

- · A relation schema R is in second normal form (2NF) if every non-prime attribute A in R is fully functionally dependent on the primary key

- · R can be decomposed into 2NF relations via the process of 2NF normalization

**Normalizing into 2NF and 3NF**

**Third Normal Form**

- · Definition:

o Transitive functional dependency: a FD X -> Z that can be derived from two FDs X -> Y and Y -> Z

- · Examples:

o SSN -> DMGRSSN is a transitive FD

§ Since SSN -> DNUMBER and DNUMBER -> DMGRSSN hold

o SSN -> ENAME is non-transitive

§ Since there is no set of attributes X where SSN -> X and X -> ENAME

- · A relation schema R is in third normal form (3NF) if it is in 2NF
*and*no non-prime attribute A in R is transitively dependent on the primary key

- · R can be decomposed into 3NF relations via the process of 3NF normalization

- · NOTE:

o In X -> Y and Y -> Z, with X as the primary key, we consider this a problem only if Y is not a candidate key.

o When Y is a candidate key, there is no problem with the transitive dependency .

o E.g., Consider EMP (SSN, Emp#, Salary ).

§ Here, SSN -> Emp# -> Salary and Emp# is a candidate key.

**Normal Forms Defined Informally**

· 1^{st} normal form

o All attributes depend on the key

· 2^{nd} normal form

o All attributes depend on the whole key

· 3^{rd} normal form

o All attributes depend on nothing but the key

**Successive Normalization of LOTS into 2NF and 3NF**

**SUMMARY OF NORMAL FORMS based on Primary Keys**

**General Normal Form Definitions (For Multiple Keys)**

· The above definitions consider the primary key only

· The following more general definitions take into account relations with multiple candidate keys

· A relation schema R is in second normal form (2NF) if every non-prime attribute A in R is fully functionally dependent on *every* key of R

· Definition:

o Superkey of relation schema R – a set of attributes S of R that contains a key of R

o A relation schema R is in third normal form (3NF) if whenever a FD X -> A holds in R, then either:

§ (a) X is a superkey of R, or

§ (b) A is a prime attribute of R

· NOTE: Boyce-Codd normal form disallows condition (b) above

**BCNF (Boyce-Codd Normal Form)**

· A relation schema R is in Boyce-Codd Normal Form (BCNF) if whenever an FD X -> A holds in R, then X is a superkey of R

· Each normal form is strictly stronger than the previous one

o Every 2NF relation is in 1NF

o Every 3NF relation is in 2NF

o Every BCNF relation is in 3NF

· There exist relations that are in 3NF but not in BCNF

· The goal is to have each relation in BCNF (or 3NF)

**Boyce-Codd Normal Form**

**A relation TEACH that is in 3NF but not in BCNF**

**Achieving the BCNF by Decomposition**

· Two FDs exist in the relation TEACH:

o fd1: { student, course} -> instructor

o fd2: instructor -> course

· {student, course} is a candidate key for this relation and that the dependencies shown follow the pattern in Figure 10.12 (b).

o So this relation is in 3NF *but not in* BCNF

· A relation NOT in BCNF should be decomposed so as to meet this property, while possibly forgoing the preservation of all functional dependencies in the decomposed relations.

o (See Algorithm 11.3)

· Three possible decompositions for relation TEACH

o {student, instructor} and {student, course}

o {course, instructor } and {course, student}

o {instructor, course } and {instructor, student}

· All three decompositions will lose fd1.

o We have to settle for sacrificing the functional dependency preservation. But we cannot sacrifice the non-additivity property after decomposition.

· Out of the above three, only the 3rd decomposition will not generate spurious tuples after join.(and hence has the non-additivity property).

· A test to determine whether a binary decomposition (decomposition into two relations) is non-additive (lossless) is discussed in section 11.1.4 under Property LJ1. Verify that the third decomposition above meets the property.

Reference : Modul_FD_dan_Normalisasi_B_Ina, Elearning UI

ENACh10_revised_sham_July13, Elearning UI

Part 6 – NORMALISASI, Agus Sanjaya

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