Normalization

  • It deals with the database design problem
  • Normalization process concerns with the transformation of the conceptual schema (logical data structure) into computer representable form.
  • It is a process of restricting data into tables; in order to ensure efficient & reliable storage & smooth retrieval of data.

Database Schema

A database schema of a database system is its structure described in a formal language supported by DBMS
Formal Language 
  •  Finite set of strings, symbols or tokens that defines a DBMS
Thus, schemas are the set of formula/rules that specify the integrity constraints imposed on Database.
Need Of Normalization
As time passes, there will be need for most databases to grow by adding new attributes and new relations. The data will be used in new ways. Tuples will be added & deleted.
Information stored will go updation also. New associations may also be added. In these suitations, the performance of the DB is dependent upon its design. A bad database design may lead to certain undesirable things like:
– Repetition of Information
– Inability to report certain information
– Loss of Info.
All this may lead to rewriting of application. Thus Normalization, helps to attain database design & ensures the efficiency of database
Advantages of Normalization
– Reduces data redundancies
– It helps in eliminating data anomalies

– It produces controlled redundancies to link tables

Database Integrity
 
    DB contained, data employed by many users. It is important that the data item & associated relation b/w them not to be destroyed. 
     The DBMS designed, includes some certain types of checks that ensures that the data entered in the table conforms to certain rules which in terms does not violates the original data structure of DB.
      Eg. No. of days an emp. Worked in a month can’t exceed the no. of days in a month.
  
First Normal Form (1NF)
A relation is in 1NF if and only if all underlying domains of each relation contain  atomic(indivisible) values, and the value of each attribute contains only a single value from that domain.
A row of data cannot contain repeating group of data i.e each column must have a unique value. Each row of data must have a unique identifier i.e Primary key. For example consider a table which is not in First normal form
1NF
  • All Key Attributes defined
  • No repeating groups in table
  • All attributes dependent on Primary Key
Second Normal Form (2NF)
Functional Dependence 
      In a given table, an attribute Y is said to have a functional depends on a set of attributes  X(X->Y)
      If and only if(iif)
      Each X value is associated with precisely one Y value
Fully Function
   
Here, is a Realation(Table),  R (Coordinate)     
R{Axis, Co-ordinate_1, Co-ordinate_2}  are its attributes

(Co-ordinate_1)  ——> (Axis) => Co-ordinate_1 is functionally dependent on Axis
(Co-ordinate_2)  ——> (Axis) => Co-ordinate_2 is functionally dependent on Axis(Co-ordinate_1)  non-dependent on (Co-ordinate_2) 

Partial Dependency  refers to the dependency of a non-key (not assigned key constraints) on the portion of the composite-primary-key and not the whole primary key.

Partial Dependency


 Hence,  

A relation R is in 2NF if and only if (iif) it is in 1NF and every non-key attribute is fully dependent on the primary key.

2NF
     

Third Normal Form (3NF)

Transitive Relation ( If A->B and B->C then A->C)

A relation R is said is said to be in 3NF iif it is in 2NF and every non-key attribute is non-transitively dependent on the primary key. 

3NF

Boyce-Codd Normal Form (BCNF)

 A relation is in BCNF if it is in 3NF and all of its determinants(i.e the attributes upon which other attributes depend) are candidate keys.

To convert a 3NF into BCNF, decompose such that every determinant becomes a Candidate Key.

 

BCNF
 

Fourth Normal Form (4NF) 

Multi valueddependencies(MVD’s)expressa Multivalued dependencies (MVD s) express a
condition among tuples of a relation that
existswhentherelationistryingtorepresent exists when the relation is trying to represent
more than one many‐many relationship

Trivial Multivalued Dependency


MVD

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