| Lesson 9 | Functional dependencies involved in normalization |
| Objective | Identify functional dependencies |
Functional Dependencies involved in Normalization
Unfortunately, there is no cut-and-dried way to identify functional dependencies.
One will have to rely on the knowledge you gain during
requirements analysis [1] to make those determinations. You may design a database for an unfamiliar company, or need to account for data on subjects about which you have little prior knowledge. The interviews you conduct and the outside reading you do are absolutely invaluable in identifying the business objects to be represented in the database and the
functional dependencies
in the resulting relations.
field is functionally dependent
One strategy you can use to determine whether a field is functionally dependent on the entire primary key is to ask if the field is an attribute of the business object represented by the table or if it is a foreign key
field used to establish a link with another table.
If neither is true, there is a good possibility the field is not functionally dependent and, therefore, the table is not in 2NF.
Representing Functional Dependencies
In relational notation, a functional dependency is represented with the
-> symbol. For example:
CustID -> CustFirst, CustLast, Address, Phone
The
-> (arrow) character is read as "determines,” so the functional dependency above is read as "CustID determines CustFirst, CustLast, Address, and Phone."
If a functional dependency has a
multi-field determinant[2], separate the fields to the left of the arrow by a comma.
An automobile insurance policy, where each policy could cover more than one car under different terms, is an example of a multi-field determinant:
PolicyNo, CarID -> Deductible, CoveragePlan
Process of Identifying Functional Dependencies
The first step is to identify the Entity Types, the sets of columns that identify them (there might be multiple) and their attributes. In this case:
Student: {StudName}, {StudNR}
attributes: StudAddr
Course: {CourseNr}, {CourseName}
Course Edition: {CourseNr, Semester, Year}
Professor: {ProfName}
From this we can derive FDs with the following rules:
(ER2FD1) If an Entity Type has keys K1 and K2, then the FD K1 -> K2 holds
(ER2FD2) If an Entity Type has a key K and single-valued attribute A then FD K -> A holds
So in this case we derive:
- StudName -> StudNR (ER2FD1)
- StudNr -> StudName (ER2FD1)
- StudNR -> StudAddr (ER2FD2)
- CourseNr -> CourseName (ER2FD1)
- CourseName -> CourseNr (ER2FD1)
The second step is to identify the Relationships, between which Entity Types they hold, and what attributes they have:
- Student-followed-Course-edition: (Student, Course Edition)
attributes: Grade
- Prof-teaches-Course-edition: (Professor, Course Edition)
From this we derive FDs with the following rules:
(ER2FD3) If a Relationship is one-to-many or one-to-one, then there holds an FD from one of the keys of the many-Entity to one of the keys of the one-Entity.
(ER2FD4) If a Relationship has a single-valued attribute, then there holds an FD from a combination of the keys of the participating Entity Types to the attribute.
So in this case we derive:
- StudNr, CourseNr, Semester, Year -> Grade (ER2FD4)
- CourseNr, Semester, Year -> ProfName (ER2FD3)
Note: We assume here that each edition only has one professor, and so Prof-teaches-Course-Edition is indeed one-to-many.
For ER2FD3 and ER2FD4 it is sufficient that this is done for only one combination of keys, since the others are implied. So we could, but do not also derive the following FDs:
- StudName, CourseNr, Semester, Year -> Grade
- StudNr, CourseName, Semester, Year -> Grade
- StudName, CourseName, Semester, Year -> Grade
The rule ER2FD3 also has a variant for n-ary relationships where n>2, which is somewhat more complex. Consider, for example, a relationship that holds between Entity Types A, B and C. Then it should be checked if perhaps one of the participating Entity Types, say C, is functionally determined by the two others, i.e., if for every combination of A entity and B entity there is at most one C entity in this relationship with them. If that is the case, then an FD should be derived from a combination of keys of A and keys of B to the keys of C. An example of this would be a relation Supplies(Supplier, Part, Project) where each Project has for each Part at most one Supplier.
Understanding Functional Dependencies
A functional dependency is a one-way relationship between two attributes such that at any given time, for each unique value of attribute A, only one value of attribute B is associated with it through the relation.
For example, assume that A is the customer number from the orders relation. Each customer number is associated with one customer first name, one last name, one street address, one city, one state, one zip code, and one phone number. Although the values for those attributes may change, at any moment, there is only one.
Functional Dependencies - Exercise
[1]Requirements analysis: The stage in the database design cycle when designers find out everything they can about the data the client needs to store in the database and the conditions under which that data needs to be accessed.
[2]multi-field determinant: A determinant consisting of more than one field.
The next lesson reviews the procedure for putting a relation in 2NF.