lossless Decomposition

What does DBMS decomposition mean?

In database management systems, the process of splitting a table into several tables or a relation into several relations is known as decomposition. When we wish to process a specific data set, we use decomposition in DBMS. When we need to guarantee consistency and eliminate anomalies and duplicate data from the database, we use a database management system. It is important to make sure that no data or information is lost during the decomposition process in DBMS.
Decomposition Types

Two categories of decomposition exist:

• Lossless Decomposition
• Lossy Decomposition
  

Lossless Decomposition: What Is It?

Lossless join decomposition is the process of breaking down a relation R into relations R1 and R2 so that the original relation R is returned when a natural join of R1 and R2 is performed. This effectively eliminates database redundancy while maintaining the original data.

Stated differently, lossless decomposition makes it possible to use joins to reconstruct the relation R from the decomposed tables R1 and R2.
For lossless join decomposition, only 1NF, 2NF, 3NF, and BCNF are valid.
The selection of a common attribute in Lossless Decomposition is based on the requirement that it be a candidate key or super key in either relation R1, R2, or both.

If at least one of the following functional dependencies is in F+ (Closure of functional dependencies), then the decomposition of a relation R into R1 and R2 is a lossless-join decomposition.

A Lossless Decomposition Example

— Employee (Employee_Id, Ename, Department_Id, Dname, Salary)
Lossless decomposition can be used to break it down as

— Department_desc (Department_Id, Dname) — Employee_desc (Employee_Id, Ename, Salary, Department_Id)
As an alternative, the lossy decomposition would be that the original data cannot be recovered because it is not possible to join these tables.

- Employee_desc (Employee_Id, Ename, Salary)
- Department_desc (Department_Id, Dname)

R1 ∩ R2 → R1 OR R1 ∩ R2 → R2 

A lossless decomposition in a database management system (DBMS) is the process of breaking down a relation schema into several relations while maintaining the data in the original relation. In particular, a lossless decomposition is one in which the decomposed relations can be joined to reconstruct the original relation.

Armstrong's axioms are a set of requirements that can be applied to achieve lossless decomposition. These requirements guarantee that all of the information contained in the original relation will be preserved in the decomposed relations. In particular, the decomposition axiom and reflexivity are the two most crucial axioms for lossless decomposition.

According to the reflexivity axiom, a larger set of attributes can be deduced from a smaller set if the former is a subset of the latter. According to the decomposition axiom, if a relation R can be broken down into two relations, R1 and R2, then the natural join of R1 and R2 can be used to reconstruct the original relation R.

The BCNF (Boyce-Codd Normal Form) and 3NF (Third Normal Form) decomposition algorithms are two of the many algorithms available for carrying out lossless decomposition in DBMS. In order to break down a relation into several relations while maintaining the ability to reconstruct the original relation with no information loss, these algorithms employ a set of rules.

Benefits of lossless decomposition

• Decreased Data Redundancy: The original relation's data redundancy is lessened thanks to lossless decomposition. By lowering storage needs and enhancing query performance, this contributes to the database system's increased efficiency.

• Updating and Maintenance: Because lossless decomposition gives you more precise control over the data, it makes it simpler to update and maintain the database.

• Better Data Integrity: By guaranteeing that each relation only includes data pertinent to that relation, breaking up a relation into smaller relations can help to improve data integrity. This can lessen errors and inconsistencies in the data.

• Increased Flexibility: By making schema modifications simpler, lossless decomposition can increase the database system's flexibility.

The drawbacks of lossless decomposition

• Enhanced Complexity: The database system may become more difficult to comprehend and administer as a result of lossless decomposition.

• Increased Processing Overhead: Breaking down a relation into smaller relations may lead to a higher processing overhead. This may result in decreased efficiency and slower query performance.

• Join Operations: In order to recover data from the decomposed relations, lossless decomposition may call for extra join operations. Slower query performance may also be the outcome of this.

• Expensive: Decomposing relations can be expensive, particularly if the database is big and intricate. Additional resources, like staff and hardware, may be needed for this. 

In conclusion

To sum up, a lossless decomposition is a crucial idea in database management systems (DBMS) that guarantees that the original relation can be rebuilt from the decomposed relations without any information loss. In practice, lossless decomposition can be accomplished with the aid of Armstrong's axioms and decomposition algorithms like BCNF and 3NF.