Decomposition in DBMS

Decomposition in Database Management Systems (DBMS) refers to the process of breaking down a relation (or table) into smaller, simpler relations while ensuring that no information is lost. Decomposition is an important technique in database normalization, where we break down large, complex tables into smaller ones that meet the criteria of normal forms (1NF, 2NF, 3NF, etc.).

The primary goal of decomposition is to eliminate redundancy, anomalies, and dependencies in the database. This process improves data integrity, query performance, and storage efficiency.

Types of Decomposition in DBMS

There are two primary types of decomposition used in DBMS:

1. Lossless Decomposition

Definition: A lossless decomposition ensures that the original relation can be perfectly reconstructed by joining the smaller relations. No data is lost during the decomposition process.

Goal: To break down a table into smaller tables, while preserving the ability to retrieve the original data without any loss of information.

Properties:

• It ensures that if you join the decomposed relations, the result will be the same as the original relation.

• It avoids the risk of losing data through incorrect decomposition.

Example:

Suppose you have a table StudentCourse:

Decomposing this into two smaller tables:

1. StudentCourse Table:

2. CourseInstructor Table:

By joining the two tables on CourseID, you can recover the original table StudentCourse.

2. Dependency-Preserving Decomposition

Definition: A dependency-preserving decomposition ensures that all the functional dependencies of the original relation are preserved in the decomposed relations. This means that no functional dependency is lost during the decomposition process.

Goal: To decompose the table in such a way that the functional dependencies remain valid and can still be enforced in the decomposed tables.

Example:

Consider a relation Employee:

Suppose the functional dependencies are:

• EmpID → EmpName

• DeptID → DeptName

We can decompose the relation into two smaller relations:

1. Employee Table:

   EmpID	EmpName
   101	Alice
   102	Bob

2. Department Table:

   DeptID	DeptName
   D001	HR
   D002	IT

This decomposition is dependency-preserving because the functional dependencies EmpID → EmpName and DeptID → DeptName are preserved in the decomposed relations.

Lossless Join and Dependency Preservation

For a decomposition to be lossless, it must satisfy the lossless join property. This property ensures that no data is lost when the decomposed tables are joined back together.

Lossless Join Property:

• Given two tables R1 and R2, a lossless join decomposition ensures that the original table R can be reconstructed without any loss of data by performing a natural join on R1 and R2.

• The key to achieving a lossless decomposition is ensuring that the intersection of the two decomposed tables contains a key from at least one of the tables. This is often ensured through the functional dependencies that the tables share.

Dependency Preservation:

• A dependency-preserving decomposition ensures that the functional dependencies of the original relation can be checked directly on the decomposed tables, without needing to join them.

• If a decomposition is dependency-preserving, then you don’t need to join the decomposed tables to enforce the original functional dependencies.

Example: Decomposition in 3NF

Let’s consider a relation Employee that we want to decompose into 3NF:

Functional Dependencies:

• EmpID → EmpName, DeptID, Manager

• DeptID → DeptName

The relation is not in 3NF because there is a transitive dependency: DeptID → DeptName (DeptID is not a superkey).

Decomposing into 3NF:

We can decompose this relation into two smaller relations:

1. Employee Table:

   EmpID	EmpName	DeptID	Manager
   101	Alice	D001	John
   102	Bob	D002	Emma

2. Department Table:

   DeptID	DeptName
   D001	HR
   D002	IT

Now, the relation is in 3NF, and the decomposition is lossless and dependency-preserving because:

• We can recover the original relation by performing a natural join between the Employee and Department tables.

• All the functional dependencies are preserved, and the data is stored more efficiently without redundancy.

Conclusion

Decomposition in DBMS is the process of breaking down large, complex tables into smaller, more manageable relations to:

• Eliminate redundancy.
• Ensure data integrity.
• Improve query performance.

Lossless decomposition ensures that no data is lost when decomposing and joining tables, while dependency-preserving decomposition ensures that the functional dependencies are maintained in the decomposed relations.