Improve Your Database with Normalization

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A quick guide to the basics of database normalization—a critical step in refreshing an older IBM i database

Editor's note: This article is excerpted from chapter 5 of SQL for IBM i: A Database Modernization Guide, by Rafael Victoria-Pereira.

Most people take a quick look at the normal forms definitions—the “steps” to achieve normalization Nirvana—and dismiss the whole thing as being an academic and convoluted waste of time. Actually, normalization is, for the most part, easy and mostly common sense with some business knowledge thrown in. Once you understand the fundamental concepts, you’ll see that it’s useful and a great way to tackle aging and “broken” databases. Let me start by introducing a few key concepts that will be used later to define each normal form.

Data Anomalies

UMADB [the example database] is already suffering from data anomalies: I’ve told you about the different “versions” of the student data found in several tables. This is being caused by structural problems in the database, which I’ll try to fix in this normalization process. But before we go any further, it’s important to define what we’re trying to fix. So, let’s take a moment to consider the different types of data anomalies, starting with the insert anomaly.

This type of anomaly occurs when a child record is inserted without a link to the parent record. For instance, creating a Grades record for a student that doesn’t exist; this can be a simple misspelling error, but it will cause an insert anomaly and put the database into an inconsistent state. However, the same thing can happen when you’re updating data: unless you have the proper safeguards in place, you can accidentally break the link between two tables, thus leaving the child table record “orphaned.” This is called an update anomaly.

Imagine that you’re updating the student information in the Classes table and inadvertently change the course name. Doing so causes the record to become orphaned, because the link to the Courses table will be compromised.

Finally, a delete anomaly occurs when you delete a parent table’s record and don’t do the same with the child’s. Because UMADB tables’ relationships are flimsy and defined at the application level, it’s very easy to mess up the database with a couple of DML statements.

These are the anomalies that we’d like to prevent. We’ll do that by applying the normal forms, as I mentioned earlier. But before that, there’s some mathematical terms you need to know.

Some Boring, Yet Important, Math Jargon

Let’s start with the simplest of them all: dependency. Dependency can come in many forms, but the easiest to understand is functional dependency: Y is functionally dependent on X if the value of Y is determined by X. In other words, if Y = X +1, the value of X will determine the resultant value of Y. Thus, Y is dependent on X as a function of the value of X.

Imagine that the university keeps a currency rates table because of its student exchange program. A sample of this table’s content, at a given time (so disregard the fact that the rates are not current), is shown in Table 1.

Table 1: Currency rates table

Currency_Code

Name

Rate

Country Name

JPY

Yen

101.689

Japan

CAD

Dollar

1.31075

Canada

AUD

Dollar

1.3217

Australia

INR

Rupee

66.725

India

NZD

Dollar

1.38535

New Zealand

GBP

Pound

0.7558

Great Britain

This table demonstrates functional dependency between the Name and Currency_Code columns: the currency name being Yen depends on the currency code being JPY.

The next notion is determinant. The determinant in the description of functional dependency in the previous paragraph is X, because X determines the value Y (at least partially because 1 is added to X as well). In Table 1, the determinant of the currency name being Rupee is the value of the currency code being INR. This means that the determinant is the currency code column. In other words, a determinant is the inversion or opposite of functional dependency.

So far, so good. Now it gets more interesting ... I hope. A transitive dependence describes the indirect dependency of a column on another: for instance, Z is transitively dependent on X when X determines Y and Y determines Z. Transitive dependence thus describes that Z is indirectly dependent on X through its relationship with Y. In Table 1, the foreign exchange rates in the Rate column (against the U.S. dollar) are dependent on the currency name (Name column). The currency name, in turn, is dependent on the country name (Country Name column). Thus, the rate is dependent on the currency, which is in turn dependent on the country name; therefore, the Rate column is transitively dependent on the Country Name column.

The next concept is something that you’re probably already familiar with: a candidate key, also known as potential or permissible key, is a field or combination of fields that can act as a primary key field for a table—thus uniquely identifying each record in the table. Most of the tables that resulted from the adjustments performed in the previous chapter have an ID column, which fits all the requirements for being a candidate key: each ID is unique within the table and is, by itself, enough to identify a record.

These ID columns actually eliminated all full functional dependencies on UMADB’s tables, because all the columns of each table depend on the primary key and this primary key is not a composite key—it’s formed by the ID column alone. For instance, if the Classes table didn’t have an ID field and its primary key was formed by the class name and class year, we could say that the course name was not fully functionally dependent of the table’s primary key, because the course name would depend only on the class name and not the class year.

However, the adjustments performed on the previous chapter didn’t solve all the database’s problems. One of the most common (and annoying, if you ask me) problems is the multi-valued dependency that exists on the Subjects_Taught column of the Teachers table. This column contains multiple values, separated by commas. These values depend on the table’s primary key as a whole. If you want to do anything with one of these values, you’ll have to isolate it from the rest of the values on the column; even so, the whole process is prone to error.

The last type of dependency doesn’t happen very often, but when it does, it’s a nightmare to untangle: cyclic dependency means that X is dependent on Y, which in turn is also dependent on X, directly or indirectly. Cyclic dependence, therefore, indicates a logically circular pattern of interdependence. Cyclic dependence typically occurs with tables containing a composite primary key of three or more fields (for example, where three fields are related in pairs to each other). In other words, X relates to Y, Y relates to Z, and X relates to Z. Ultimately Z relates back to X. This is not very common, but I’ve seen it happen in tables with complex keys and multiple identifying relationships to other equally complex tables.

These notions may seem farfetched and pointless now, but you’ll see how the normal forms relate to them and how this can be of use when “tidying up” a database.

Introducing the Normal Forms, Academic Version

The steps to achieving Nirvana are long and hard ... wait, wrong book. No, they’re actually simple and a very acceptable. A normalization pseudo-Nirvana state can be achieved with only three steps, explained next. Unlike the steps in other paths to enlightenment, these have logical, cold, and simple names (they were defined by the academic community, so what else could we expect?).

  • First normal form (1NF)—Eliminate repeating groups so that all records in all tables can be identified uniquely by a primary key in each table. In other words, all fields other than the primary key must depend on the primary key.
  • Second normal form (2NF)—All non-key values must be fully functionally dependent on the primary key. No partial dependencies are allowed. A partial dependency exists when a field is fully dependent on a part of a composite primary key.
  • Third normal form (3NF)—Eliminate transitive dependencies, meaning that a field is indirectly determined by the primary key. This is because the field is functionally dependent on another field, whereas the other field is dependent on the primary key.

We’ll be implementing these three steps in UMADB during this chapter, but the normalization path doesn’t end here. It goes further with (even more) convoluted requirements:

  • Boyce-Codd normal form (BCNF)—Every determinant in a table is a candidate key. If there is only one candidate key, BCNF and 3NF are one and the same.
  • Fourth normal form (4NF)—Eliminate multiple sets of multi-valued dependencies.
  • Fifth normal form (5NF)—Eliminate cyclic dependencies. 5NF is also known as projection normal form (PJNF).
  • Domain key normal form (DKNF)—DKNF is the ultimate application of normalization and is more a measurement of conceptual state, as opposed to a transformation process in itself. It’s normalization Nirvana.

You might be wondering why we’ll stop at 3NF when the rest of the normal forms seem accessible. Well, the problem is that the higher the normalization state is, the harder it gets to query the database. This happens because higher normalization states cause more data fragmentation (read: more tables), and this affects performance. And we all know that a database with poor performance is not really useful. That’s enough theory; let’s apply the normal forms to UMADB!

Normalizing UMADB to 3NF

1NF is easy to understand, but sometimes it’s not so easy to apply. In UMADB’s case, a quick review of the tables shows that only the Classes table contains repeating groups of columns: the class name and class year columns have repeating values, one per each student who attended a certain class in a certain year. The first step is fixing this issue, by “exploding” this table into three tables and adding information: one of the class definitions, which will contain the class name; a link to the course table and a description; table two with the class for a given year, containing the teacher name; and finally, a third table for student enrollment in that class/year combination.

2NF is somewhat similar to 1NF, but at value level, as opposed to 1NF’s column level. There’s only one example of columns holding multiple values: the Subjects_Taught column in the Teachers table. The logical thing to do would be to create a many-to-many relationship, because a teacher can teach many subjects and a subject can be taught by many teachers, but in practice many-to-many relationships should be avoided at all costs. They are conceptually sane, but hard to understand and maintain in a real database. A many-to-many relationship would imply creating a Subjects table and linking it to the existing Teachers table. Instead, we’ll include an intermediate table, named Subjects_Taught, and create one-to-many relationships with both the existing Teachers table and the new Subjects table.

3NF is not so easy to explain. Even if you understand what a transitive dependency is, it can be hard to identify it in a database. Let me give you a hand: I started this chapter by referring to some duplicate data across the database and went on to explain how and why this can cause data anomalies. The student data exists in multiple tables, but, in most cases, it shouldn’t because it doesn’t depend directly on the table’s primary key. For instance, a student’s home address shouldn’t depend on the class he/she is taking. Instead, it should depend on the student information stored in the Students table. However, a closer look at the Students and Teachers tables reveals that they have a lot of information in common—after all, both students and teachers are people. This means that it might be a good idea to strip these tables of the information about a person that they contain and centralize that data in a new Persons table. Naturally, the partial information contained in the Classes table should also be eliminated and replaced with a link to the respective student record.

We’ll also create new tables for the Department (only its name exists in the Courses table, which can lead to confusing situations) and Teacher Rank, to avoid inconsistencies. Finally, we’ll introduce referential integrity to this database (at the moment, all the connections between tables are kept at the application level, and, from what we’ve seen, it’s not working properly) by replacing the weak links (name references, mostly, such as the student name in the Classes table) with proper foreign keys.

In summary, here’s what we’ll have to do:

  1. Create new tables for Class Definitions, Classes per Year, Class Enrollment, Subjects, Subjects Taught, Persons, Departments, and Teacher Ranks.
  2. Remove duplicate columns, related with student data, in the Students, Teachers, and Classes tables.
  3. Create proper foreign keys to link all the “informally linked” existing tables and link the new tables as well.

We could continue to change the tables the same way we’ve been doing so far—using DROP and CREATE TABLE statements. However, there are a lot of changes and it’s going to be hard to keep track of everything. Instead, we’ll “do it like the pros” and use a data-modeling tool.

 

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