Relational model
Relational Model represents how data is stored in Relational Databases. A relational database stores data in the form of relations (tables). Consider a relation STUDENT with attributes ROLL_NO, NAME, ADDRESS, PHONE and AGE shown in Table.
STUDENT
| ROLL_NO | NAME | ADDRESS | PHONE | AGE |
| 1 | Ram | Dharan | 9455123451 | 18 |
| 2 | Ramesh | Gorkha | 9652431543 | 18 |
| 3 | Sujit | Pokhara | 9156253131 | 20 |
| 4 | Suresh | Kathmandu | 18 |
The relational model consists of three major components:
1. The set of relations and set of domains that defines the way data can be represented (data structure).
2. Integrity rules that define the procedure to protect the data (data integrity).
3. The operations that can be performed on data (data manipulation).
Important terminologies
- Attribute: Attributes are the properties that define a relation. e.g.; ROLL_NO, NAME
- Relation Schema: A relation schema represents name of the relation with its attributes. e.g.; STUDENT (ROLL_NO, NAME, ADDRESS, PHONE and AGE) is relation schema for STUDENT. If a schema has more than 1 relation, it is called Relational Schema.
- Tuple: Each row in the relation is known as tuple.
- Relation Instance: The set of tuples of a relation at a particular instance of time is called as relation instance. It can change whenever there is insertion, deletion or updation in the database.
- Degree: The number of attributes in the relation is known as degree of the relation.
- Cardinality: The number of tuples in a relation is known as cardinality.
- Column: Column represents the set of values for a particular attribute.
- NULL Values: The value which is not known or unavailable is called NULL value. It is represented by blank space.
Pitfalls in Relational DB Design
A bad design may have several properties, including:
- Repetition of information.
- Inability to represent certain information.
- Loss of information
- hardware overhead
Anomalies: Anomalies are those unexpected and integrity error that occur due to the flaws or limitation of given database.There are three types of anomalies .They are
- Insertion anomaly: It occurs while inserting one fact in the database requires unnecessary knowledge of other facts being inserted.
- Deletion anomaly: It occurs while deleting one fact from database causes loss of other unrelated data.
- Update anomaly: It occurs while updating the values of one fact requires multiple changes to the database.
Functional dependencies
It is a relationship between columns X and Y such that given value of X can determine the value of Y
i.e X → Y where , X is determinant of Y and Y is functionally dependent.
Partial dependency:It occurs when a column in a table only depends on a part of concatenated keys.
Transitive dependency: It occurs when non-key attribute is functionally dependent on one or more non-key attribute.
Closure of functional dependency
Closure of a set (x+) is the set of attribute functionally determined by x.
Let S be the set of functional dependencies on a relation R. Let x is set of attributes that appear on left hand side of same functional dependencies in S and we want to determine the set of all attributes that are dependent on x. Thus for such set of attribute x, we determine the set x+ of attribute that are functionally algorithm to find closure of functional dependency. Each determined by x based on S, x+ is called closure of x under S.
Algorithm to find closure of functional dependency is
x+=x;
Repeat
Old x+=x+
Do
If Y is subset of x+ then,
x+=x+U z
until (x+=old x+)
/* don’t change then leave loop */
Closure of attribute set
suppose we are given relation R with attributes (A,B,C,D) and FDS A→BC, B→CD. Find the closure attribute of A.
we have,
A+=A;
A(BC) as A →BC
AB(CD)C as
ABCDC = ABCD
So, A+=ABCD
Application of closure set of attributes
- It is used to identify the additional functional dependencies
- It is used to identify keys (candidate key and super key)
- It is used to identify the prime and non-prime attribute
- It is used to identify equivalence of functional dependencies
Decomposition
Decomposition in database means breaking tables down into multiple tables. If the relation has no proper decomposition, then it may lead to problems like loss of information. Decomposition is used to eliminate some of the problems of bad design like anomalies, inconsistencies, and redundancy.
Types of Decomposition
Lossless join decomposition:If the information is not lost from the relation that is decomposed, then the decomposition will be lossless. The lossless decomposition guarantees that the join of relations will result in the same relation as it was decomposed. The relation is said to be lossless decomposition if natural joins of all the decomposition give the original relation.
Dependency preserving: In the dependency preservation, at least one decomposed table must satisfy every dependency. If a relation R is decomposed into relation R1 and R2, then the dependencies of R either must be a part of R1 or R2 or must be derivable from the combination of functional dependencies of R1 and R2.
For example, suppose there is a relation R (A, B, C, D) with functional dependency set (A->BC). The relational R is decomposed into R1(ABC) and R2(AD) which is dependency preserving because FD A->BC is a part of relation R1(ABC).
Normalization
It is the process of decomposing relations with anomalies to produce smaller, well-structured relations that
- save typing of repetitive data
- reduce disk space
- to ease data manipulation
- avoid frequent restructuring of tableBenefits
- less storage space
- quicker update
- clearer data relationship
- easier to add
- flexible structure
- less data inconsistencyFirst Normal Form (1NF)
Each column is unique in 1NF.
As per the rule of first normal form, an attribute (column) of a table cannot hold multiple values. It should hold only atomic values.
Example: 1
Sample Employee table, it displays employees are working with multiple departments.
| Employee | Age | Department |
| Milan | 32 | Marketing, Sales |
| Ram | 45 | Quality Assurance |
| Krishna | 36 | Human Resource |
Employee table following 1NF:
| Employee | Age | Department |
| Milan | 32 | Marketing |
| Milan | 32 | Sales |
| Ram | 45 | Quality Assurance |
| Krishna | 36 | Human Resource |
Example 2: Suppose a company wants to store the names and contact details of its employees. It creates a table that looks like this:
| emp_id | emp_name | emp_address | emp_mobile |
| 101 | Hari | Dharan | 8912312390 |
| 102 | John | Kathmandu | 8812121212 9900012222 |
| 103 | Radha | Pokhara | 7778881212 |
| 104 | Seema | Bandipur | 9990000123 8123450987 |
this table is not in 1NF as the rule says “each attribute of a table must have atomic (single) values”, the emp_mobile values for employees John & Seema violates that rule.
To make the table complies with 1NF we should have the data like this:
| emp_id | emp_name | emp_address | emp_mobile |
| 101 | Hari | Dharan | 8912312390 |
| 102 | John | Kathmandu | 8812121212 |
| 102 | John | Kathmandu | 9900012222 |
| 103 | Radha | Pokhara | 7778881212 |
| 104 | Seema | Bandipur | 9990000123 |
| 104 | Seema | Bandipur | 8123450987 |
Example:- 3
Student Table :
| Student | Age | Subject |
| Adam | 15 | Biology, Maths |
| Alex | 14 | Maths |
| Stuart | 17 | Maths |
In First Normal Form, any row must not have a column in which more than one value is saved, like separated with commas. Rather than that, we must separate such data into multiple rows.
Student Table following 1NF will be :
| Student | Age | Subject |
| Adam | 15 | Biology |
| Adam | 15 | Maths |
| Alex | 14 | Maths |
| Stuart | 17 | Maths |
Using the First Normal Form, data redundancy increases, as there will be many columns with same data in multiple rows but each row as a whole will be unique.
Second Normal Form (2NF)
The entity should be considered already in 1NF and all attributes within the entity should depend solely on the unique identifier of the entity.
Example: 1 Sample Products table:
| productID | product | Brand |
| 1 | Monitor | Apple |
| 2 | Monitor | Samsung |
| 3 | Scanner | HP |
| 4 | Head phone | JBL |
Product table following 2NF:
Products Category table:
| productID | product |
| 1 | Monitor |
| 2 | Scanner |
| 3 | Head phone |
Brand table:
| brandID | Brand |
| 1 | Apple |
| 2 | Samsung |
| 3 | HP |
| 4 | JBL |
Products Brand table:
| pbID | productID | brandID |
| 1 | 1 | 1 |
| 2 | 1 | 2 |
| 3 | 2 | 3 |
| 4 | 3 | 4 |
Example 2: Suppose a school wants to store the data of teachers and the subjects they teach. They create a table that looks like this: Since a teacher can teach more than one subjects, the table can have multiple rows for a same teacher.
| teacher_id | Subject | teacher_age |
| 111 | Maths | 38 |
| 111 | Physics | 38 |
| 222 | Biology | 38 |
| 333 | Physics | 40 |
| 333 | Chemistry | 40 |
Candidate Keys: {teacher_id, subject}
Non prime attribute: teacher_age
he table is in 1 NF because each attribute has atomic values. However, it is not in 2NF because non prime attribute teacher_age is dependent on teacher_id alone which is a proper subset of candidate key. This violates the rule for 2NF as the rule says “no non-prime attribute is dependent on the proper subset of any candidate key of the table”.
To make the table complies with 2NF we can break it in two tables like this:
teacher_details table:
| teacher_id | teacher_age |
| 111 | 38 |
| 222 | 38 |
| 333 | 40 |
teacher_subject table:
| teacher_id | Subject |
| 111 | Maths |
| 111 | Physics |
| 222 | Biology |
| 333 | Physics |
| 333 | Chemistry |
Now the tables comply with Second normal form (2NF).
Third Normal form (3NF)
A table design is said to be in 3NF if both the following conditions hold:
- Table must be in 2NF
- Transitive functional dependency of non-prime attribute on any super key should be removed.
An attribute that is not part of any candidate key is known as non-prime attribute.
In other words 3NF can be explained like this: A table is in 3NF if it is in 2NF and for each functional dependency X-> Y at least one of the following conditions hold:
- X is a super key of table
- Y is a prime attribute of table
An attribute that is a part of one of the candidate keys is known as prime attribute.
Example: Suppose a company wants to store the complete address of each employee, they create a table named employee_details that looks like this:
| emp_id | emp_name | emp_zip | emp_state | emp_city | emp_district |
| 1001 | John | 282005 | UP | Agra | Dayal Bagh |
| 1002 | Ajeet | 222008 | TN | Chennai | M-City |
| 1006 | Lora | 282007 | TN | Chennai | Urrapakkam |
| 1101 | Lilly | 292008 | UK | Pauri | Bhagwan |
| 1201 | Steve | 222999 | MP | Gwalior | Ratan |
Super keys: {emp_id}, {emp_id, emp_name}, {emp_id, emp_name, emp_zip}…so on
Candidate Keys: {emp_id}
Non-prime attributes: all attributes except emp_id are non-prime as they are not part of any candidate keys.
Here, emp_state, emp_city & emp_district dependent on emp_zip. And, emp_zip is dependent on emp_id that makes non-prime attributes (emp_state, emp_city & emp_district) transitively dependent on super key (emp_id). This violates the rule of 3NF.
To make this table complies with 3NF we have to break the table into two tables to remove the transitive dependency:
employee table:
| emp_id | emp_name | emp_zip |
| 1001 | John | 282005 |
| 1002 | Ajeet | 222008 |
| 1006 | Lora | 282007 |
| 1101 | Lilly | 292008 |
| 1201 | Steve | 222999 |
employee_zip table:
| emp_zip | emp_state | emp_city | emp_district |
| 282005 | UP | Agra | Dayal Bagh |
| 222008 | TN | Chennai | M-City |
| 282007 | TN | Chennai | Urrapakkam |
| 292008 | UK | Pauri | Bhagwan |
| 222999 | MP | Gwalior | Ratan |
Boyce Codd normal form (BCNF)
It is an advance version of 3NF that’s why it is also referred as 3.5NF. BCNF is stricter than 3NF. A table complies with BCNF if it is in 3NF and for every functional dependency X->Y, X should be the super key of the table.
Example: Suppose there is a company wherein employees work in more than one department. They store the data like this:
| emp_id | emp_nationality | emp_dept | dept_type | dept_no_of_emp |
| 1001 | Austrian | Production and planning | D001 | 200 |
| 1001 | Austrian | stores | D001 | 250 |
| 1002 | American | design and technical support | D134 | 100 |
| 1002 | American | Purchasing department | D134 | 600 |
Functional dependencies in the table above:
emp_id -> emp_nationality
emp_dept -> {dept_type, dept_no_of_emp}
Candidate key: {emp_id, emp_dept}
The table is not in BCNF as neither emp_id nor emp_dept alone are keys.
To make the table comply with BCNF we can break the table in three tables like this:
emp_nationality table:
| emp_id | emp_nationality |
| 1001 | Austrian |
| 1002 | American |
emp_dept table:
| emp_dept | dept_type | dept_no_of_emp |
| Production and planning | D001 | 200 |
| Stores | D001 | 250 |
| design and technical support | D134 | 100 |
| Purchasing department | D134 | 600 |
emp_dept_mapping table:
| emp_id | emp_dept |
| 1001 | Production and planning |
| 1001 | Stores |
| 1002 | design and technical support |
| 1002 | Purchasing department |
Functional dependencies:
emp_id -> emp_nationality
emp_dept -> {dept_type, dept_no_of_emp}
Candidate keys:
For first table: emp_id
For second table: emp_dept
For third table: {emp_id, emp_dept}
This is now in BCNF as in both the functional dependencies left side part is a key.