1. Eliminate Repeating Groups – Make a separate table for each set of
related attributes, and give each table a primary key.
2. Eliminate Redundant Data – If an attribute depends on only part of a
multi-valued key, remove it to a separate table.
3. Eliminate Columns Not Dependent On Key – If attributes do not
contribute to a description of the key, remove them to a separate
4. Isolate Independent Multiple Relationships – No table may contain two
or more 1:n or n:m relationships that are not directly related.
5. Isolate Semantically Related Multiple Relationships – There may be
practical constrains on information that justify separating logically
related many-to-many relationships.
6. Optimal Normal Form – a model limited to only simple (elemental)
facts, as expressed in ORM.
7. Domain-Key Normal Form – a model free from all modification anomalies.
1. Eliminate Repeating Groups
In the original member list, each member name is followed by any databases
that the member has experience with. Some might know many, and others might
not know any. To answer the question, “Who knows DB2?” we need to perform
an awkward scan of the list looking for references to DB2. This is
inefficient and an extremely untidy way to store information.
Moving the known databases into a seperate table helps a lot. Separating
the repeating groups of databases from the member information results in
first normal form. The MemberID in the database table matches the primary
key in the member table, providing a foreign key for relating the two
tables with a join operation. Now we can answer the question by looking in
the database table for “DB2” and getting the list of members.
2. Eliminate Redundant Data
In the Database Table, the primary key is made up of the MemberID and the
DatabaseID. This makes sense for other attributes like “Where Learned” and
“Skill Level” attributes, since they will be different for every
member/database combination. But the database name depends only on the
DatabaseID. The same database name will appear redundantly every time its
associated ID appears in the Database Table.
Suppose you want to reclassify a database – give it a different DatabaseID.
The change has to be made for every member that lists that database! If you
miss some, you’ll have several members with the same database under
different IDs. This is an update anomaly.
Or suppose the last member listing a particular database leaves the group.
His records will be removed from the system, and the database will not be
stored anywhere! This is a delete anomaly. To avoid these problems, we need
second normal form.
To achieve this, separate the attributes depending on both parts of the key
from those depending only on the DatabaseID. This results in two tables:
“Database” which gives the name for each DatabaseID, and “MemberDatabase”
which lists the databases for each member.
Now we can reclassify a database in a single operation: look up the
DatabaseID in the “Database” table and change its name. The result will
instantly be available throughout the application.
3. Eliminate Columns Not Dependent On Key
The Member table satisfies first normal form – it contains no repeating
groups. It satisfies second normal form – since it doesn’t have a
multivalued key. But the key is MemberID, and the company name and location
describe only a company, not a member. To achieve third normal form, they
must be moved into a separate table. Since they describe a company,
CompanyCode becomes the key of the new “Company” table.
The motivation for this is the same for second normal form: we want to
avoid update and delete anomalies. For example, suppose no members from the
IBM were currently stored in the database. With the previous design, there
would be no record of its existence, even though 20 past members were from
4. Isolate Independent Multiple Relationships
This applies primarily to key-only associative tables, and appears as a
ternary relationship, but has incorrectly merged 2 distinct, independent
The way this situation starts is by a business request list the one shown
below. This could be any 2 M:M relationships from a single entity. For
instance, a member could know many software tools, and a software tool may
be used by many members. Also, a member could have recommended many books,
and a book could be recommended by many members.
Initial business request
So, to resolve the two M:M relationships, we know that we should resolve
them separately, and that would give us 4th normal form. But, if we were to
combine them into a single table, it might look right (it is in 3rd normal
form) at first. This is shown below, and violates 4th normal form.
To get a picture of what is wrong, look at some sample data, shown below.
The first few records look right, where Bill knows ERWin and recommends the
ERWin Bible for everyone to read. But something is wrong with Mary and
Steve. Mary didn’t recommend a book, and Steve Doesn’t know any software
tools. Our solution has forced us to do strange things like create dummy
records in both Book and Software to allow the record in the association,
since it is key only table.
Sample data from incorrect solution
The correct solution, to cause the model to be in 4th normal form, is to
ensure that all M:M relationships are resolved independently if they are
indeed independent, as shown below.
Correct 4th normal form
NOTE! This is not to say that ALL ternary associations are invalid. The
above situation made it obvious that Books and Software were independently
linked to Members. If, however, there were distinct links between all
three, such that we would be stating that “Bill recommends the ERWin Bible
as a reference for ERWin”, then separating the relationship into two
separate associations would be incorrect. In that case, we would lose the
distinct information about the 3-way relationship.
5. Isolate Semantically Related Multiple Relationships
OK, now lets modify the original business diagram and add a link between
the books and the software tools, indicating which books deal with which
software tools, as shown below.
Initial business request
This makes sense after the discussion on Rule 4, and again we may be
tempted to resolve the multiple M:M relationships into a single
association, which would now violate 5th normal form. The ternary
association looks identical to the one shown in the 4th normal form
example, and is also going to have trouble displaying the information
correctly. This time we would have even more trouble because we can’t show
the relationships between books and software unless we have a member to
link to, or we have to add our favorite dummy member record to allow the
record in the association table.
The solution, as before, is to ensure that all M:M relationships that are
independent are resolved independently, resulting in the model shown below.
Now information about members and books, members and software, and books
and software are all stored independently, even though they are all very
much semantically related. It is very tempting in many situations to
combine the multiple M:M relationships because they are so similar. Within
complex business discussions, the lines can become blurred and the correct
solution not so obvious.
Correct 5th normal form
6. Optimal Normal Form
At this point, we have done all we can with Entity-Relationship Diagrams
(ERD). Most people will stop here because this is usually pretty good.
However, another modeling style called Object Role Modeling (ORM) can
display relationships that cannot be expressed in ERD. Therefore there are
more normal forms beyond 5th. With Optimal Normal Form (OMF)
It is defined as a model limited to only simple (elemental) facts, as
expressed in ORM.
7. Domain-Key Normal Form
This level of normalization is simply a model taken to the point where
there are no opportunities for modification anomalies.
. “if every constraint on the relation is a logical consequence of the
definition of keys and domains”
. Constraint “a rule governing static values of attributes”
. Key “unique identifier of a tuple”
. Domain “description of an attribute’s allowed values”
1. A relation in DK/NF has no modification anomalies, and conversely.
2. DK/NF is the ultimate normal form; there is no higher normal form
related to modification anomalies
3. Defn: A relation is in DK/NF if every constraint on the relation is a
logical consequence of the definition of keys and domains.
4. Constraint is any rule governing static values of attributes that is
precise enough to be ascertained whether or not it is true
5. E.g. edit rules, intra-relation and inter-relation constraints,
functional and multi-valued dependencies.
6. Not including constraints on changes in data values or time-dependent
7. Key – the unique identifier of a tuple.
8. Domain: physical and a logical description of an attributes allowed
9. Physical description is the format of an attribute.
10. Logical description is a further restriction of the values the domain
11. Logical consequence: find a constraint on keys and/or domains which,
if it is enforced, means that the desired constraint is also enforced.
12. Bottom line on DK/NF: If every table has a single theme, then all
functional dependencies will be logical consequences of keys. All data
value constraints can them be expressed as domain constraints.
13. Practical consequence: Since keys are enforced by the DBMS and domains
are enforced by edit checks on data input, all modification anomalies
can be avoided by just these two simple measures.