Decomposition in DBMS | Lossless | Lossy

Decomposition of a Relation-

 

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-

 

1. Lossless decomposition-

 

Lossless decomposition ensures-

  • 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.

 

2. Dependency Preservation-

 

Dependency preservation ensures-

  • None of the functional dependencies that holds on the original relation are lost.
  • The sub relations still hold or satisfy the functional dependencies of the original relation.

 

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 )-

 

ABC
121
253
333

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-

 

AB
12
25
33

R1( A , B )

 

BC
21
53
33

R2( B , C )

 

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-

 

ABC
121
253
333

 

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 following relation R( A , B , C )-

 

ABC
121
253
333

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-

 

AC
11
23
33

R1( A , B )

 

BC
21
53
33

R2( B , C )

 

Now, let us check whether this decomposition is lossy or not.

For lossy decomposition, we must have-

R1 ⋈ R2 ⊃ R

 

Now, if we perform the natural join ( ⋈ ) of the sub relations R1 and Rwe get-

 

ABC
121
253
233
353
333

 

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.

 

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.

 

Next Article- Rules to Determine Lossless and Lossy Decomposition

 

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Summary
Decomposition in DBMS | Lossless | Lossy
Article Name
Decomposition in DBMS | Lossless | Lossy
Description
Decomposition in DBMS is a process of dividing a relation into sub relations. Types of Decomposition in DBMS- Lossless Decomposition and Lossy Decomposition.
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Gate Vidyalay
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