Difference between Lossless and Lossy Join Decomposition

The process of breaking up a relation into smaller sub-relations is called Decomposition. Decomposition is required in DBMS to convert a relation into a specific normal form which further reduces redundancy, anomalies, and inconsistency in the relation. 

There are mainly two types of decompositions in DBMS 

1. Lossless join Decomposition
2. Lossy join Decomposition  

Lossless Join Decomposition

Lossless join decomposition is a process in which a relation is decomposed into smaller relations without losing any information. When we rejoin the decomposed relations, the original relation is perfectly reconstructed without losing data.

Advantages of Lossless Join Decomposition

• Data Integrity: On decomposed tables no loss of any data or information when re-join them together, it becomes the original table before decomposition.
• Consistency: This decomposition ensures that data will remain accurate and consistent across the database.
• Normalization: This helps in achieving higher normal forms like 3NF or BCNF and improving efficiency.

Disadvantage of Lossless Join Decomposition

• Storage Overhead: Storage usage is increased, as sometimes additional tables and columns are needed.
• Complex Queries: To rejoin the table we decomposed may require complex SQL queries, and these queries may impact the performance.

Lossy Join Decomposition

In this type of decomposition the information will be lost if the relations are decomposed into smaller parts. This means that when the original relation is decomposed and then later we try to rejoin them back together then some data from the original relation is not lost and not recoverable, which leads to data inconsistencies.

Advantages of Lossy Join Decomposition

• Structure is Simple, the result of decomposing the relations will give simple and smaller sub tables and this helps in reducing the complexity in some cases.
• Redundancy is Less: In some cases where loss of information is acceptable will help in reducing redundancy in certain cases.

Disadvantage of Lossy Join Decomposition

• Loss of Data: When tables are joined back together then some of the information will be loosed permanently which can cause problem.
• Inconsistency: as discussed above, due to information loss the data integrity problem will arise.
• Hard to manage: It can be difficult to maintain data consistency as some information may loss, which is making harder to manage the database.

Difference Between Lossless and Lossy Join Decomposition

Example-1: 
Example to check whether given Decomposition Lossless Join Decomposition. 

Let there be a relational schema Student(Roll No., S_name, S_dept). StudentDetails(Roll No., S_name) and Dept(Roll No., S_dept) be it's decompositions. 

Now for the decomposition to be lossless, 

StudentDetails ⨝ Dept = Student then, StudentDetails ⨝ Dept  is

As, StudentDetails ⨝ Dept = Student, 

This decomposition is Lossless. 

Example-2: 
Example to check whether given Decomposition Lossy Join Decomposition. 

Let there be a relational schema Student(Roll No., S_name, S_dept). StudentDetails(Roll No., S_name) and Dept(S_name, S_dept) be it's decompositions. 

Now for the decomposition to be lossy, 

Student ⊂ StudentDetails ⨝ Dept then, StudentDetails ⨝ Dept  is

As, Student ⊂ StudentDetails ⨝ Dept, 

This decomposition is Lossy. 
Thus, we can figure out whether decomposition is lossless or lossy.

Conclusion

Based on the specific needs of the database we need to choose the correct decomposition method. Lossless Join Decomposition is preferred when loosing the data is not acceptable and as it ensures no data is lost, then data integrity is maintained. It is essential for databases that prioritize data accuracy and completeness, such as financial systems or healthcare records, ensures that no critical data is lost, maintaining system efficiency.

However, Lossy join Decomposition is acceptable where little bit of data loss or information loss is tolerable but also helps in reducing the redundancy of data which is more important than loosing the information. So, understanding them will help to choose them wisely according on the specific needs of the system and its data requirements.