What is Multi-valued dependency and why MVD is needed

Multivalued Dependency in Normalization

What is multivalued dependency (MVD)?

A multivalued dependency (MVD) is a type of database dependency that occurs when one attribute in a relation determines multiple independent sets of values for another attribute. It represents a situation where two attributes are not functionally dependent, but are independently determined by a third attribute.

Formal Definition

In a relation R, a multivalued dependency A ↠ B (↠ the symbol is referred as 'multi-determines') exists if for each value of A, the set of values of B is independent of the other attributes (say C) in the relation.

This means A ↠ B implies A determines multiple values of B, regardless of other attributes.

Example

Consider a student who may learn multiple programming languages and play multiple sports — both independently.

Student	Language	Sport
Ravi	Java	Cricket
Ravi	Python	Cricket
Ravi	Java	Badminton
Ravi	Python	Badminton

Here:

For Student = Ravi, 

• Languages = {Java, Python}

• Sports = {Cricket, Football}

Language and Sport are independent, but both depend on Student.

So, we have:

                            Student ↠ Language
                            Student ↠ Sport

This is a classic multivalued dependency.

Why MVD matters?

Multivalued dependencies lead to data redundancy and anomalies.

To remove these anomalies, a relation with non-trivial MVDs should be decomposed into 4th Normal Form (4NF).

Example decomposition:

R(Student, Language, Sport) ⟶

R1(Student, Language)
R2(Student, Sport)