Chapter 13
Further Normalization
II: Higher Normal
Forms
Topics in this Chapter
• Multi-Valued Dependencies and Fourth
Normal Form
• Join Dependencies and Fifth Normal Form
• The Normalization Procedure Summarized
• A Note on Denormalization
• Orthogonal Design
• Other Normal Forms
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.
13-2
Multi-Valued Dependencies and Fourth
Normal Form
• A multi-valued dependency occurs when a
determinant determines more than one
dependent, and the dependents are
independent of each other
• Ex.: course implies teacher; course implies
text, where teacher and text are independent
• A relvar with course, teacher and text is all
key, and exhibits redundancy, but is in 3NF
• Updates can exhibit anomalies
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.
13-3
Fourth Normal Form
• Relvar R is in 4 NF if and only if, whenever
there exist subsets A and B of the attributes of
R such that the nontrivial multi-valued
dependency A multi-determines B is satisfied,
then all attributes of R are also functionally
dependent on A
• In the previous example, decompose course,
teacher, text into two relvars: course teacher,
and course text
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.
13-4
Join Dependencies and Fifth Normal Form
• There exist relvars that cannot be nonlossdecomposed into two relvars, but can be
nonloss-decomposed into more than two
• Ex.: supplier, part, project
• A supplier supplies parts and projects, a
project is supplied by suppliers and parts, but
from this you may not validly conclude that a
particular supplier supplies a particular part to
a particular project
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.
13-5
Join Dependency
• Let R be a relvar, and let A, B, … Z be subsets
of the attributes of R. Then we say that R
satisfies the JD
* ( A, B, …. Z )
if and only if every legal value of R is equal to
the join of its projections on A, B, … Z
• Supplier, part, project can be said to satisfy
this only if an additional constraint is included
to make the specific conclusion valid
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.
13-6
Fifth Normal Form
• A relvar R is in 5NF – also called projectionjoin normal form, if and only if every
nontrivial join dependency that is satisfied by
R is implied by the candidate key(s) of R
• In the general case, SPJ is not in 5NF, but SP,
PJ, and JS are in 5NF
• 5NF is a generalization of 4NF, which is a
generalization of 3NF
• It is the most general form possible for
projection-based normalization
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.
13-7
The Normalization Procedure Summarized
• Begin with a relvar in 1NF
• Take projections to eliminate FDs that are not
irreducible; result is in 2NF
• Take projections to eliminate transitive FDs;
result is in 3NF
• Take projections to eliminate FDs in which
the determinant is not a candidate key; result
is BCNF
• Continue on next slide
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.
13-8
The Normalization Procedure Continued
• Using a relvar in BCNF, take projections to
eliminate MVDs that are not also FDs
• In practice it is unlikely that you will need to
do this, because you will have eliminated
independent relation valued attributes before
you began
• Take projections of 4NF relvars to eliminate
JDs that are not implied by the candidate keys,
if you can find any
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.
13-9
Normalization Steps
• By definition 5NF is the final normal form for
decompositions based on projection
• All anomalies are a result of FDs or MVDs or
JDs that are not implied by the candidate keys
• Mathematical relations are complete in 1NF;
successive steps are needed because database
relations are semantic: they are based on the
real world meaning of the data
• If you design well from the top, the design
will be normalized from the beginning
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.
13-10
A Note on Denormalization
• Denormalization is said to be necessary to
improve performance
• Technically normalization is a model concept,
not related to stored files
• Most people confuse the two, as a shorthand
• In practice, denormalization will speed up
some queries, and drag down others
• Proceed with caution
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.
13-11
Orthogonal Design
• Within a given database, no two distinct base
relvars should have overlapping meanings
• Let A and B be distinct base relvars. Then
there must not exist nonloss decompositions
of A and B into A1, A2 …, Am and B1, B2,
…, Bn such that some projection of Ai in the
set A1, A2, …, Am and some projection of Bj
in the set B1, B2, …, Bn have overlapping
meanings
• Base relvars should have mutually
independent meanings
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.
13-12
Other Normal Forms
• Additional normal forms arise in the analysis
of dependency theory
• Domain-key normal form (DK/NF) is not
defined in terms of FDs, MVDs, or JDs
• A relvar R is in DK/NF if and only if every
constraint on R is a logical consequence of the
domain constraints and key constraints that
apply to R
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.
13-13
Yet More Normal Forms
• Restriction-union normal form applies when
we segment the relvar horizontally, i.e. via
restriction rather than projection
• Sixth normal form represents a generalization
of join dependency, which would require a
generalization of the projection and join
operators
• By definition, a relvar in 6NF is in 5NF
• Further research on dependency theory is
underway
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.
13-14