Lec-28: Lossless and Lossy Decomposition| Fifth (5th) Normal Form | Database Management System

Summary

This video explains the concepts of lossless and lossy decomposition in database normalization. It highlights the importance of preserving data consistency during table decomposition. The video discusses how to decompose a table into smaller sub-tables, ensuring that common attributes, such as candidate keys, are preserved. It demonstrates how using a natural join can help recombine the tables, but warns that improper decomposition may lead to lossy decomposition, where extra, inconsistent tuples are introduced. Key conditions for ensuring lossless decomposition, including the candidate key condition and non-empty intersection, are also covered.

Takeaways

• 😀 Lossless decomposition ensures that when a table is decomposed, no information is lost. It is essential for maintaining data integrity.
• 😀 Lossy decomposition, on the other hand, may introduce extra or spurious tuples, leading to inconsistency in the database.
• 😀 A valid decomposition should always have at least one common attribute between the decomposed tables to allow for future joins.
• 😀 When decomposing a table, it is important to ensure that the common attribute is a candidate key or a super key of either or both decomposed tables.
• 😀 The natural join operation is crucial for rejoining decomposed tables. It combines the tables based on equal values of the common attribute.
• 😀 When performing a natural join, the result includes only rows where the values of the common attribute are equal in both tables.
• 😀 Lossy decomposition leads to inconsistencies because extra rows (spurious tuples) are introduced, violating the original data integrity.
• 😀 Lossless join decomposition ensures that when the tables are recombined, they accurately represent the original data, with no spurious rows.
• 😀 For a decomposition to be lossless, the union of attributes from both tables should be equivalent to the original table's attributes.
• 😀 The intersection of attributes between the decomposed tables must not be empty to ensure a valid decomposition and prevent loss of information.
• 😀 A correct decomposition uses candidate keys or super keys as common attributes, preventing the introduction of duplicate or inconsistent data.

Q & A

What is the key difference between lossless and lossy decomposition?

The key difference is that **lossless decomposition** allows for the original data to be perfectly reconstructed after rejoining the decomposed tables, without any loss of information. On the other hand, **lossy decomposition** results in extra or spurious tuples after rejoining, leading to inconsistencies in the database.

Why must there be at least one common attribute between the decomposed tables?

There must be at least one common attribute between the decomposed tables to allow for proper rejoining in case a query requires it. Without a common attribute, there would be no way to relate the two tables, making it impossible to reconstruct the original data.

What role does the candidate key play in ensuring lossless decomposition?

The common attribute in the decomposed tables must be a **candidate key** or **super key** of either or both tables. This ensures that the attribute uniquely identifies tuples and avoids duplications, which is critical to achieving lossless decomposition.

What happens if we choose a non-candidate key as the common attribute in decomposition?

If a non-candidate key is chosen as the common attribute, it could introduce **duplicacy** and lead to **lossy decomposition**, where extra or spurious tuples appear after rejoining, causing inconsistency in the database.

Can you explain the concept of 'spurious tuples' in the context of lossy decomposition?

Spurious tuples are extra rows that appear after performing a lossy decomposition and rejoining the tables. These rows do not exist in the original table and cause inconsistency because they do not reflect the true data, leading to flawed queries and results.

What is the purpose of performing normalization in a database?

Normalization in a database is aimed at reducing redundancy and improving data integrity by organizing data into smaller, related tables. This is achieved through processes like decomposition, ensuring the database adheres to specific normal forms.

What is the condition for a lossless decomposition when using the union of attributes from two decomposed tables?

For a lossless decomposition, the **union** of the attributes from the decomposed tables must be equivalent to the set of attributes in the original table. This ensures that the decomposition retains all the original data without loss.

What does the intersection condition state in the context of decomposition?

The intersection condition states that when decomposing a table, the intersection of the decomposed tables must not be empty. This ensures that there is at least one common attribute, which is necessary to rejoin the tables later.

What is the role of a natural join in the decomposition process?

A **natural join** is used to combine the decomposed tables based on their common attribute. It automatically filters rows where the values of the common attribute match in both tables, allowing us to merge them while removing redundant data.

How does choosing an incorrect common attribute lead to lossy decomposition?

Choosing an incorrect common attribute, especially one that is not a candidate key, can introduce rows that don't belong in the original table. This results in spurious tuples when the tables are rejoined, leading to **lossy decomposition**, which is problematic due to data inconsistency.