Multivalued Dependency in Database Design

Multivalued dependency breaks fourth normal form

Network connection
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In a relational database, a dependency occurs when the information stored in the same database table uniquely determines other information stored in the same table. A multivalued dependency occurs when the presence of one or more rows in a table implies the presence of one or more other rows in that same table. Put another way, two attributes (or columns) in a table are independent of one another, but both depend on a third attribute.

A multivalued dependency prevents the normalization standard fourth normal form (4NF). Relational databases follow five normal forms that represent guidelines for record design. They prevent update anomalies and inconsistencies in the data. The fourth normal form deals with many-to-one relationships in a database.

Functional Dependency vs. Multivalued Dependency

To understand a multivalued dependency, it is helpful to revisit what a functional dependency is.

If an attribute X uniquely determines an attribute Y, then Y is functionally dependent on X. This is written as X -> Y. For example, in the Students table below, the Student_Name determines the Major:

RaviArt History

This functional dependency can be written:  Student_Name -> Major. Each  Student_Name determines exactly one Major and no more.

If you want the database to also track the sports these students take, you might think the easiest way to do this is to just add another column titled Sport:

RaviArt HistorySoccer
RaviArt HistoryVolleyball
RaviArt HistoryTennis

The problem here is that both Ravi and Beth play multiple sports. It is necessary to add a new row for every additional sport. 

This table has introduced a multivalued dependency because the major and the sport are independent of one another but both depend on the student.

This is a simple example and easily identifiable, but a multivalue dependency could become a problem in a large, complex database.

A multivalued dependency is written X ->-> Y. In this case:

Student_Name  ->-> Major
Student_Name  ->-> Sport

This is read as "Student_Name multidetermines Major" and "Student_Name multidetermines Sport."

A multivalued dependency always requires at least three attributes because it consists of at least two attributes that are dependent on a third.

Multivalued Dependency and Normalization

A table with a multivalued dependency violates the normalization standard of Fourth Normal Form (4NK) because it creates unnecessary redundancies and can contribute to inconsistent data. To bring this up to 4NF, it is necessary to break this information into two tables.

The table below now has a functional dependency of Student_Name -> Major, and no multivalued dependencies:

Students & Majors
RaviArt History
RaviArt History
RaviArt History


While this table also has a single functional dependency of Student_Name -> Sport:

Students & Sports


It's clear that normalization is often addressed by simplifying complex tables so that they contain information related to a single idea or theme rather than trying to make a single table contain too much disparate information.