Multivalued Dependency and Fourth Normal Form

In database management systems, normalization is an essential process to ensure that data is organized efficiently and effectively. Multivalued dependency (MVD) is a concept that helps to identify and eliminate data redundancy and anomalies, and Fourth Normal Form (4NF) is a normalization form that addresses the challenges associated with multivalued dependency.

In this article, we will discuss multivalued dependency, Fourth Normal Form, and their importance in database management systems.

Normalization

Normalization is a process of organizing data in a database to reduce redundancy and improve data integrity. The normalization process involves dividing a database into two or more tables and establishing relationships between them. The first three normal forms, 1NF, 2NF, and 3NF, help to eliminate redundancy and improve data integrity by breaking up the data into smaller, more manageable tables. Boyce-Codd Normal Form (BCNF) is a stricter form of the 3NF, which further eliminates anomalies associated with functional dependencies.

Multivalued Dependency (MVD)

Multivalued dependency (MVD) is a type of dependency that exists when a table contains more than one multivalued attribute, and changes to one attribute can affect another attribute. In other words, MVD occurs when a table has a non-trivial relationship between attributes that are not part of the same composite key.

For example, consider a table called "Students". It has columns: "Student ID," "Course," and "Textbook." Each student can take multiple courses, and each course may require multiple textbooks. Therefore, the "Course" and "Textbook" columns are multivalued attributes.

Student ID	Course	Textbook
1	Math	Algebra
1	Math	Calculus
2	Science	Biology
2	Science	Chemistry
2	Art	Art History
3	History	American History

In this example, we can note that there is a relationship between the "Course" and "Textbook" columns. The "Course" column determines which textbooks are needed. For example, a student taking "Math" will need both "Algebra" and "Calculus" textbooks. This relationship between "Course" and "Textbook" is a multivalued dependency.

To express this MVD, we can write the following formula:

Course →→ Textbook

This indicates that for any given value of "Course," there is a set of corresponding values of "Textbook." For example, if we know that a student is taking "Math," we can infer that the student needs both "Algebra" and "Calculus" textbooks.

MVD occurs when a table has a non-trivial relationship between attributes that are not part of the same composite key. In the example above, the "Course" and "Textbook" columns have a multivalued dependency because the "Course" column determines which textbooks are needed.

Fourth Normal Form (4NF)

Fourth Normal Form (4NF) is a level of database normalization that requires a relation to be in BCNF and have no non-trivial multivalued dependencies other than the candidate key, to eliminate redundant data and maintain data consistency. If a table violates this standard, it needs to be split into two tables to achieve 4NF.

For a relation R to be in 4NF, it must meet two conditions −

• It should be in Boyce-Codd Normal Form (BCNF).

• It should not have any non-trivial multivalued dependencies.

To remove the multivalued dependency (MVD) in the "Students" table example, we can create two new tables, one for "Courses" and another for "Textbooks," and establish a relationship between them using foreign keys.

Here's how we can create the tables:

Table 1: Students

Student ID	Course ID
1	1
1	2
2	3
2	4
2	5
3	6

Table 2: Courses

Course ID	Course Name
1	Math
2	Science
3	Art
4	History

Table 3: Textbooks

Textbook ID	Textbook Name	Course ID
1	Algebra	1
2	Calculus	2
3	Biology	2
4	Chemistry	2
5	Art History	3
6	American History	4

So, we removed the multivalued dependency by splitting the "Course" and "Textbook" columns into separate tables.

We have also added a new "Course ID" column to the "Students" table. It has a foreign key that references the "Course ID" column in the "Courses" table. Similarly, the "Textbooks" table also has a "Course ID" column that serves as a foreign key referencing the "Course ID" column in the "Courses" table.

Hence, we have achieved the fourth normal form (4NF) for the "Students" table. It has done after by removing the multivalued dependency and creating separate tables. The Resultant schema eliminates data redundancy and improves data integrity, making it easier to manage and query the database.

Challenges of Fourth Normal Form

Achieving 4NF can be challenging, as it requires careful analysis of functional dependencies, selecting appropriate keys, and balancing between normalization and performance. Achieving 4NF can be time-consuming, and it may require additional storage space.

Techniques for Achieving Fourth Normal Form

There are several techniques for achieving 4NF, including using a join dependency, splitting tables, and using an intersection table. Analyzing functional dependencies is critical in achieving 4NF. Partial dependencies and transitive dependencies need to be identified and eliminated.

Examples of Achieving Fourth Normal Form

An example of achieving 4NF is splitting a table with MVDs into two or more tables, with each table containing attributes that are functionally dependent on the primary key. In another example, an intersection table can be used to eliminate MVDs by creating a separate table that links two other tables with MVDs.

Conclusion

Multivalued dependency is a concept which can be removed by 4NF. 4NF helps to eliminate data redundancy, improve data integrity, and improve database performance. Achieving 4NF can be challenging. But it improves data quality, better database performance, and less anomalies associated that has data redundancy. By analyzing functional dependencies and using appropriate techniques, 4NF can be achieved.