Functional dependencies are a fundamental concept in database design, and are used to establish relationships between attributes in a database. They are used to ensure that the database is in a state of normalization, which helps to minimize data redundancy and improve data integrity.
What are functional dependecies?
A functional dependency is a relationship between two sets of attributes in a database, where one set (the determinant) determines the values of the other set (the dependent). For example, in a database of employees, the employee ID number (determinant) would determine the employee’s name, address, and other personal information (dependent). This means that, given an employee ID number, we can determine the corresponding employee’s name and other personal information, but not vice versa.
Functional dependencies can also be represented using mathematical notation. For example, the functional dependency above can be represented as:
Employee ID → Employee Name, Address, etc.
It’s important to note that functional dependencies only apply to the individual tuples in the table, and not to the table as a whole.
What can functional dependencies be used for?
Identify and eliminate data redundancy in a database
For example, if a database contains a table with the attributes “employee ID” and “employee name”, and another table with the attributes “employee ID” and “employee address”, then there is a functional dependency between “employee ID” and “employee name” in the first table, and between “employee ID” and “employee address” in the second table.
By combining these two tables into one, with the attributes “employee ID”, “employee name”, and “employee address”, the data redundancy is eliminated.
Identify and eliminate data inconsistencies in a database
For example, if a database contains a table with the attributes “employee ID” and “employee name”, and another table with the attributes “employee ID” and “employee address”, then there is a functional dependency between “employee ID” and “employee name” in the first table, and between “employee ID” and “employee address” in the second table. If the employee’s name is changed in the first table, but not in the second table, then the data is inconsistent.
By combining these two tables into one, with the attributes “employee ID”, “employee name”, and “employee address”, the data inconsistencies are eliminated.
What are the different types of functional dependencies?
There are several types of functional dependencies, including full functional dependencies, partial functional dependencies, and transitive functional dependencies.
A full functional dependency is a functional dependency where the dependent attributes are determined by the determinant attributes. For example, in the database of employees, the employee ID number fully determines the employee’s name, address, and other personal information.
A partial functional dependency is a functional dependency where the dependent attributes are partially determined by the determinant attributes. For example, in a database of employees, the employee ID number may partially determine the employee’s address, but not the employee’s name or other personal information.
A transitive functional dependency is a functional dependency where the dependent attributes are determined by a set of attributes that are not included in the determinant attributes. For example, in a database of employees, the employee ID number may determine the employee’s department, which in turn determines the employee’s salary.
Functional dependencies are a crucial aspect of database design and are used to ensure that the database is in a state of normalization. They help to minimize data redundancy and improve data integrity. However, it’s important to note that functional dependencies are not the only factor to consider when designing a database. Other factors such as performance and scalability should also be taken into account.
One of the most common ways to represent functional dependencies is using the Armstrong’s Axioms. These are a set of rules that can be used to infer functional dependencies from a given set of functional dependencies. These rules include reflexivity, augmentation, and transitivity.
Reflexivity states that if X is a subset of Y, then Y → X.
Augmentation states that if X → Y, then XZ → YZ for any attributes Z.
Transitivity states that if X → Y and Y → Z, then X → Z.
Normal forms in functional dependencies
Another way to represent functional dependencies is using the Normal Forms. Normal Forms are a set of rules that are used to determine the degree of normalization of a database. There are several Normal Forms, including First Normal Form (1NF), Second Normal Form (2NF), Third Normal Form (3NF), and so on.
First Normal Form (1NF) requires that each table have a primary key, and that all data in the table is atomic (indivisible).
Second Normal Form (2NF) requires that the table is in 1NF, and that all non-primary key attributes are functionally dependent on the primary key.
Third Normal Form (3NF) requires that the table is in 2NF, and that all non-primary key attributes are not functionally dependent on any non-primary key attributes.
It’s important to note that functional dependencies are not always easy to identify, and may require a thorough understanding of the data and the relationships between the data. Additionally, it’s not always possible to achieve higher Normal Forms, and trade-offs may need to be made between normalization and performance.
Conclusion
Functional dependencies are a crucial aspect of database design and are used to ensure that the database is in a state of normalization. They help to minimize data redundancy and improve data integrity. However, it’s important to note that functional dependencies are not the only factor to consider when designing a database. Other factors such as performance and scalability should also be taken into account.
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