BCNF

Boyce-Codd Normal Form (BCNF) is a database normalization technique used to eliminate data redundancy and improve data integrity in a relational database. It is a more strict form of normalization than Third Normal Form (3NF).

To be in BCNF, a table must first meet the requirements of First Normal Form (1NF), Second Normal Form (2NF), and Third Normal Form (3NF). The fourth requirement for BCNF is that for every functional dependency A → B (where A and B are sets of attributes), A must be a superkey of the table.

To illustrate this, let’s consider an example of a table called “Employees” with columns “EmployeeID,” “DepartmentID,” “DepartmentName,” and “DepartmentManager.” The primary key is the “EmployeeID” column, and the “DepartmentID” column is a foreign key referencing the “Departments” table.

However, the “DepartmentManager” attribute depends only on the “DepartmentID” attribute, and not on the entire composite primary key. This violates the BCNF requirement because “DepartmentID” is not a superkey of the “Employees” table.

To normalize the table to BCNF, we would split it into two separate tables: “Employees” and “Departments.” The “Employees” table would have columns “EmployeeID” and “DepartmentID,” while the “Departments” table would have columns “DepartmentID,” “DepartmentName,” and “DepartmentManager.”

By doing this, we ensure that every functional dependency in the “Employees” table has a superkey on the left-hand side, eliminating data redundancy and improving data integrity in our database.

Multi-valued dependencies and fifth Normal Forms

Multi-Valued Dependencies (MVDs) are a type of dependency in a relational database where the values of one set of attributes may have multiple, independent values for another set of attributes. Fifth Normal Form (5NF) is a normalization technique used to eliminate data redundancy and improve data integrity in a relational database that involves MVDs.

To illustrate MVDs, let’s consider an example of a table called “Orders” with columns “OrderID,” “CustomerID,” “CustomerName,” “ProductID,” “ProductName,” and “ProductAttributes.” In this example, “ProductAttributes” is a set of attributes that can have multiple, independent values for each “ProductID.”

For example, if “ProductID” is “P1,” “ProductAttributes” may have multiple values for “Color,” “Size,” and “Weight.” This means that there is an MVD between “ProductID” and “ProductAttributes.”

To normalize the table to 5NF, we would split it into four separate tables: “Orders,” “Customers,” “Products,” and “ProductAttributes.” The “Orders” table would have columns “OrderID,” “CustomerID,” and “ProductID,” while the “Customers” table would have columns “CustomerID” and “CustomerName,” and the “Products” table would have columns “ProductID” and “ProductName.”

The “ProductAttributes” table would have columns “ProductID,” “AttributeName,” and “AttributeValue.” Each row in the “ProductAttributes” table would represent a single attribute-value pair for a specific “ProductID.”

By doing this, we ensure that each attribute is dependent on the primary key or other non-key attributes, eliminating data redundancy and improving data integrity in our database. In addition, by separating out the “ProductAttributes” into its own table, we can handle MVDs in a normalized and efficient way.