Lossless 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.
Example
Consider the following table:
EMPLOYEE_DEPARTMENT table
| EMP_ID | EMP_NAME | EMP_AGE | EMP_CITY | DEPT_ID | DEPT_NAME |
|---|---|---|---|---|---|
| 22 | Denim | 28 | Mumbai | 827 | Sales |
| 33 | Alina | 25 | Delhi | 438 | Marketing |
| 46 | Stephan | 30 | Bangalore | 869 | Finance |
| 52 | Katherine | 36 | Mumbai | 575 | Production |
| 60 | Jack | 40 | Noida | 678 | Testing |
It can be decomposed into:
EMPLOYEE table:
| EMP_ID | EMP_NAME | EMP_AGE | EMP_CITY |
|---|---|---|---|
| 22 | Denim | 28 | Mumbai |
| 33 | Alina | 25 | Delhi |
| 46 | Stephan | 30 | Bangalore |
| 52 | Katherine | 36 | Mumbai |
| 60 | Jack | 40 | Noida |
DEPARTMENT table:
| DEPT_ID | EMP_ID | DEPT_NAME |
|---|---|---|
| 827 | 22 | Sales |
| 438 | 33 | Marketing |
| 869 | 46 | Finance |
| 575 | 52 | Production |
| 678 | 60 | Testing |
Thus, the join on these relations on EMP_ID will generate the same relation as the decomposed one.
Determine Decomposition Is Lossless Or Lossy
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.
Example
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).