Lossy and Lossless Decomposition in DBMS
Decomposition plays a crucial role in structuring relational databases. Understanding the concepts of lossy and lossless decomposition is essential for maintaining data integrity and optimizing database design. Let's delve into these concepts and explore their significance in Database Management System (DBMS).
Consider this relation is decomposed into two sub relations as R1( A , C ) and R2( B , C )-
This relation is not same as the original relation R and contains some extraneous tuples.
Clearly, R1 ⋈ R2 ⊃ R. Thus, we conclude that the above decomposition is lossy join decomposition.
 |
| Lossy and Lossless Decomposition in DBMS |
Decomposition in DBMS
Definition: The process of breaking up or dividing a single relation into two or more sub relations is called as decomposition of a relation.Properties of Decomposition:
The following two properties must be followed when decomposing a given relation-- No information is lost from the original relation during decomposition.
- When the sub relations are joined back, the same relation is obtained that was decomposed. Every decomposition must always be lossless.
Types of Decomposition
Decomposition of a relation can be completed in the following two ways:
1. Lossless Join Decomposition
- Consider there is a relation R which is decomposed into sub relations R1 , R2 , …. , Rn.
- This decomposition is called lossless join decomposition when the join of the sub relations results in the same relation R that was decomposed.
- For lossless join decomposition, we always have-
R1 ⋈ R2 ⋈ R3 ……. ⋈ Rn = R
where ⋈ is a natural join operator.
Example:
Consider the following relation R( A , B , C )-
Consider this relation is decomposed into two sub relations R1( A , B ) and R2( B , C )-
The two sub relations are-
Now, let us check whether this decomposition is lossless or not. For lossless decomposition, we must have-
R1 ⋈ R2 = R
Now, if we perform the natural join ( ⋈ ) of the sub relations R1 and R2 , we get-
Now, if we perform the natural join ( ⋈ ) of the sub relations R1 and R2 , we get-
This relation is same as the original relation R. Thus, we conclude that the above decomposition is lossless join decomposition.
Note
- Lossless join decomposition is also known as non-additive join decomposition. This is because the resultant relation after joining the sub relations is same as the decomposed relation.
- No extraneous tuples appear after joining of the sub-relations.
2. Lossy Join Decomposition
- Consider there is a relation R which is decomposed into sub relations R1 , R2 , …. , Rn.
- This decomposition is called lossy join decomposition when the join of the sub relations does not result in the same relation R that was decomposed.
- The natural join of the sub relations is always found to have some extraneous tuples.
- For lossy join decomposition, we always have-
R1 ⋈ R2 ⋈ R3 ……. ⋈ Rn ⊃ R
where ⋈ is a natural join operator.Example:
Consider the above relation R( A , B , C )Consider this relation is decomposed into two sub relations as R1( A , C ) and R2( B , C )-
The two sub relations are-
Now, let us check whether this decomposition is lossy or not.
For lossy decomposition, we must have-
For lossy decomposition, we must have-
R1 ⋈ R2 ⊃ R
Now, if we perform the natural join ( ⋈ ) of the sub relations R1 and R2 we get-
Clearly, R1 ⋈ R2 ⊃ R. Thus, we conclude that the above decomposition is lossy join decomposition.
Note
- Lossy join decomposition is also known as careless decomposition.
- This is because extraneous tuples get introduced in the natural join of the sub-relations.
- Extraneous tuples make the identification of the original tuples difficult.
Also Read: Lossless Decomposition in DBMS
