Lossless Join and Dependency Preserving Decomposition in DBMS

Lossless join and dependency-preserving decomposition are important concepts in database management systems (DBMS).

Lossless Join Decomposition

 In a database system, a relationship between two or more tables can be represented as a join operation. Decomposition is the process of breaking down a large table into smaller, more manageable tables. Lossless join decomposition ensures that the information in the original table can be reconstructed from the smaller tables without loss of information. In other words, when the smaller tables are joined, the result is equivalent to the original table.

How to check for lossless join decomposition using FD set, which conditions must hold

To check for lossless join decomposition using functional dependencies (FDs), two conditions must hold:

• The decomposed must be a union-compatible decomposition. This means that the attributes in the decomposed tables must correspond to a subset of the attributes in the original table, and the common attributes must be a super key in the decomposed tables. In other words, the decomposed must be such that the original table can be reconstructed by taking the union of the decomposed tables.
• The decomposed must not introduce any extraneous information. This means that the FDs in the decomposed tables must be a subset of the FDs in the original table. In other words, the decomposed must preserve all functional dependencies in the original table.

If these two conditions hold, then the decomposed is considered a lossless join decomposition. If either condition is not met, the decomposition is not considered lossless, as information may be lost or extraneous information may be introduced during the reconstruction of the original table.

Example of Lossless Join Decomposition

Here's a simple example of lossless join decomposition:

Consider a table named "Orders" with the following attributes: OrderID, CustomerID, ProductID, Quantity, and OrderDate.

We can decompose this table into two smaller tables: "Order" and "OrderLine".

The "Order" table will contain the OrderID, CustomerID, and OrderDate attributes.

The "OrderLine" table will contain the OrderID, ProductID, and Quantity attributes.

The two smaller tables can be joined on the OrderID attribute to recreate the original "Orders" table. This is considered a lossless join decomposition because all the information in the original table can be reconstructed without loss of information.

Dependency-Preserving Decomposition

Dependency-Preserving Decomposition is a technique used in database management to decompose a large database into smaller, more manageable parts while preserving the relationships (dependencies) between the data in the original database. The objective of this technique is to minimize the loss of information or functional dependencies among the attributes in the decomposed database.

In this process, the original database is divided into multiple smaller components, called projections. These projections contain a subset of the original attributes and preserve the dependencies among the attributes in each projection. This decomposition process helps to reduce the complexity of the database and improve the efficiency of database queries by allowing the database administrator to retrieve information from a smaller and more manageable part of the database, rather than from the entire database.

Dependency-Preserving Decomposition is particularly useful in data warehousing and data mining applications, where large amounts of data need to be managed and analyzed efficiently. By preserving the dependencies between the data in the decomposed, the technique ensures that the information in the decomposed is consistent and complete, and that queries on the decomposed will produce accurate results

Dependenciesbetween attributes in the original table are maintained in the smaller tables after decomposition.

In a database system, functional dependencies between attributes can be used to preserve the relationships between attributes in the original table after decomposition. A functional dependency exists when the value of one attribute determines the value of another attribute.

For example, consider the "Orders" table from the previous example: OrderID, CustomerID, ProductID, Quantity, and OrderDate. There is a functional dependency between the OrderID and CustomerID attributes, meaning that the value of OrderID determines the value of CustomerID.

In the decomposed of the "Orders" table into the "Order" and "OrderLine" tables, the functional dependency between the OrderID and CustomerID attributes can be preserved by ensuring that the OrderID attribute is included in both the "Order" and "OrderLine" tables. In other words, the OrderID attribute serves as the common key between the two smaller tables.

By preserving the functional dependencies in this way, the relationships between the attributes in the original table are maintained in the decomposed tables, ensuring that the information in the original table can be reconstructed without loss of information. This is known as dependency-preserving decomposition

In summary, lossless join decomposition ensures that the information in the original table can be reconstructed without loss of information, while dependency-preserving decomposition ensures that the functional dependencies in the original table are preserved in the decomposed.

Difference between Lossless Join and Dependency preserving Decomposition in DBMS

Here's a comparison of lossless join decomposition and dependency preserving decomposition in tabular form:

In short, lossless join decomposition ensures that the information in the original table can be reconstructed without loss of information, while dependency preserving decomposition ensures that the functional dependencies in the original table are preserved in the decomposed