Lossless Decomposition, Lossless Join ,and Dependency Preserving Decomposition, Denormalization

Lossless Decomposition in DBMS:

Lossless decomposition, also known as lossless join or lossless-join decomposition, is a property that ensures that when a relation (table) is decomposed into smaller relations, and you perform a natural join on those smaller relations, you can recreate the original relation without losing any information. In other words, it guarantees that no data is lost during the decomposition process.

There are two main criteria for a decomposition to be lossless:

1. Union Property (Covering Property): The union of the decomposed relations should be equal to the original relation. In other words, all the rows in the original relation should be preserved in the decomposition.

2. Intersection Property: The common attributes (keys) shared between the decomposed relations should form a superkey for at least one of the decomposed relations. This ensures that you can uniquely identify and combine rows from different decomposed relations without ambiguity.

Achieving lossless decomposition is crucial to maintain data integrity and ensure that you can reconstruct the original data without errors.

Lossless Join and Dependency Preserving Decomposition:

Lossless join and dependency-preserving decomposition are related concepts in database design. In addition to ensuring that no data is lost during decomposition (lossless), dependency preservation aims to maintain functional dependencies that exist in the original relation after decomposition.

A decomposition is considered dependency preserving if it preserves all the functional dependencies of the original relation in at least one of the decomposed relations. This means that any functional dependency that held in the original relation will also hold in one of the decomposed relations.

Denormalization in Databases with Examples:

Denormalization is the process of intentionally introducing redundancy into a relational database by incorporating data from related tables into one table. This is done to improve query performance or simplify complex queries at the cost of increased storage space and some data maintenance challenges.

Here's an example to illustrate denormalization:

Consider a normalized database for an e-commerce website. You have two tables: Customers and Orders.

Table: Customers

CustomerID	CustomerName	CustomerEmail
101	Alice	[e-mail]
102	Bob	[e-mail]
103	Carol	[e-mail]

Table: Orders

OrderID	CustomerID	OrderDate	TotalAmount
1	101	2023-01-15	100.00
2	102	2023-02-10	75.00
3	101	2023-03-20	50.00

In a normalized database, you keep customer information separate from order information to avoid redundancy. However, if you frequently need to retrieve customer information along with their orders, it might be inefficient to perform multiple joins.

To denormalize, you can create a single table that combines customer and order information:

Denormalized Table: CustomersWithOrders

CustomerID	CustomerName	CustomerEmail	OrderID	OrderDate	TotalAmount
101	Alice	[e-mail]	1	2023-01-15	100.00
102	Bob	[e-mail]	2	2023-02-10	75.00
103	Carol	[e-mail]	3	2023-03-20	50.00

By denormalizing in this way, you can simplify queries for reporting purposes, especially when you need to retrieve customer and order data together. However, you should carefully consider the trade-offs, such as increased storage requirements and potential data update anomalies, when denormalizing a database.