Multivalued Dependency

Multivalued Dependency

In the world of relational databases, Multivalued Dependency (MVD) is a concept that extends beyond basic functional dependencies. It plays a crucial role in understanding data redundancy and achieving higher levels of normalization.

What is a Multivalued Dependency?

When two attributes in a database depend on a third attribute yet are independent of one another, this is known as a multivalued dependency. This dependency involves at least three attributes, with one acting as a common determinant for the other two.

Multivalued dependencies arise as a consequence of the First Normal Form (1NF), which restricts an attribute in a tuple from having a set of values. To represent multiple values, repeated combinations of independent attributes are stored—leading to multivalued dependencies.

In simpler terms, when a single attribute determines multiple independent facts, each of which can take on multiple values, a multivalued dependency is present.

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Functional vs. Multivalued Dependency

• A value of attribute A is mapped to a single value of attribute B by a functional dependency, which is represented as A → B.
• A value of attribute A is mapped to several values of attribute B in a multivalued dependency (shown as A →→ B), where the values are independent of other attributes in the relation.

Example 1: Bike Manufacturer

Consider a company that manufactures bikes in two colors (white and black) for each model and each manufacturing year. Below is the table structure:

Here, both MANUF_YEAR and COLOR are dependent on BIKE_MODEL but are independent of each other. This makes COLOR and MANUF_YEAR multivalued dependent on BIKE_MODEL.

These dependencies are represented as:

• BIKE_MODEL →→ MANUF_YEAR
• BIKE_MODEL →→ COLOR

This means that for each bike model, all valid combinations of year and color must be stored.

Example 2: Staff Information

Consider a relation that records staff members, the equipment they are assigned, and the languages they speak:

In this table:

• A staff member can have multiple pieces of equipment.
• A staff member can be fluent in multiple languages.
• Equipment and Language are independent of each other, but both are dependent on S_Name.

So, the multivalued dependencies are:

• S_Name →→ Equipment
• S_Name →→ Language

To represent all combinations, we need to list every pairing of Equipment and Language for each staff member.

Properties of Multivalued Dependency

Understanding the nature of MVDs requires knowing their key properties:

1. At least three attributes are needed
   MVDs cannot exist with only two attributes. The third attribute ensures that two dependent attributes are being compared for independence.
2. Independence of dependent attributes
   The attributes on the right-hand side of MVDs must not depend on each other.
3. Pairs of dependencies exist
   If A →→ B holds, then typically another MVD like A →→ C will also exist in the same relation.
4. Functional dependency as a special case
   If a multivalued dependency results in only one value, it behaves like a functional dependency. In essence, functional dependency is a subset of multivalued dependency.

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Final Thoughts

Multivalued dependencies are a fundamental part of understanding database normalization beyond 1NF and 2NF. They help identify hidden redundancies and lead to better data modeling through Fourth Normal Form (4NF).

By identifying and resolving multivalued dependencies, database designers can build more efficient, accurate, and maintainable data structures.

For more foundational and advanced database concepts, stay connected with UpdateGadh—your trusted source for technical learning.

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