Multivalued Dependency in Database Design

Multivalued dependency breaks fourth normal form

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.

Scrolling through a database looking for donors who might make good board members.
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A multivalued dependency prevents the normalization standard fourth normal form. 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:

Student_Name Major
Ravi Art History
Beth Chemistry

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:

Student_Name Major Sport
Ravi Art History Soccer
Ravi Art History Volleyball
Ravi Art History Tennis
Beth Chemistry Tennis
Beth Chemistry Soccer

The problem here is that both Ravi and Beth play several 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 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:

Student_Name Major
Ravi Art History
Ravi Art History
Ravi Art History
Beth Chemistry
Beth Chemistry
Students & Majors

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

Student_Name Sport
Ravi Soccer
Ravi Volleyball
Ravi Tennis
Beth Tennis
Beth Soccer
Students & Sports

Normalization is often accomplished 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.

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