Chapter 7: Relational Database Design

Chapter 7: Relational Database DesignChapter 7: Relational Database Design

©Silberschatz, Korth and Sudarshan7.2Database System Concepts


ExampleR = ( student_id, student_name, course_id, course_name )

F = { student_id student_name,

course_id course_name }

{ student_id, course_id } is a candidate key.

Fc = F

R1 = ( student_id, student_name )

R2 = ( course_id, course_name )

R3 = ( student_id, course_id)


Example 2

R = ( A, B, C )

F = { A BC, B C }R is not in 3NF

Fc = { A B, B C }

Decomposition into: R1 = ( A, B ), R2 = ( B, C )

R1 and R2 are in 3NF


BCNF VS 3NFBCNF VS 3NF

always possible to decompose a relation into relations in 3NF and the decomposition is lossless dependencies are preserved

always possible to decompose a relation into relations in BCNF and the decomposition is lossless may not be possible to preserve dependencies


Candidate keys are (sid, part_id)

and (sname, part_id).

{ sid, part_id } qty{ sname, part_id } qtysid snamesname sid

The relation is in 3NF:

For sid sname, … sname is in a candidate key.

For sname sid, … sid is in a candidate key.

However, this leads to redundancy and loss of information

More ExamplesMore Examples

SSP

sid

sname part_id

qty


If we decompose the schema into

R1 = ( sid, sname ), R2 = ( sid, part_id, qty )These are in BCNF.

The decomposition is dependency preserving.{ sname, part_id } qty can be deduced from

(1) sname sid (given)(2) { sname, part_id } { sid, part_id } (augmentation on (1))(3) { sid, part_id } qty (given)

and finally transitivity on (2) and (3).

SSP

sid

sname part_id

qty


At a city, for a certain part, the supplier is unique:city part_id sid.Also, sid city

The relation is not in BCNF:sid city is not trivial, and … sid is not a superkey

It is in 3NF:sid city … city is in the candidate key of { city, part_id }.

If we decompose into ( sid, city ) and ( sid, part_id ) we have BCNF, however { city, part_id } sid will not be preserved.

SUPPLY

part_id

SUPPLY city part_id sid

city sidMore Examples


Design GoalsDesign Goals

Goal for a relational database design is: BCNF lossless join Dependency preservation

If we cannot achieve this, we accept: 3NF lossless join Dependency preservation


Multivalued DependenciesMultivalued Dependencies There are database schemas in BCNF that do not seem to be

sufficiently normalized Consider a database

classes(course, teacher, book)such that (c,t,b) classes means that t is qualified to teach c, and b is a required textbook for c

The database is supposed to list for each course the set of teachers any one of which can be the course’s instructor, and the set of books, all of which are required for the course (no matter who teaches it).


There are no non-trivial functional dependencies and therefore the relation is in BCNF

Insertion anomalies – i.e., if Sara is a new teacher that can teach database, two tuples need to be inserted

(database, Sara, DB Concepts)(database, Sara, Ullman)

course teacher book

databasedatabasedatabasedatabasedatabasedatabaseoperating systemsoperating systemsoperating systemsoperating systems

AviAviHankHankSudarshanSudarshanAviAvi Jim Jim

DB ConceptsUllmanDB ConceptsUllmanDB ConceptsUllmanOS ConceptsShawOS ConceptsShaw

classes

Multivalued Dependencies (Cont.)Multivalued Dependencies (Cont.)


Therefore, it is better to decompose classes into:

course teacher

databasedatabasedatabaseoperating systemsoperating systems

AviHankSudarshanAvi Jim

teaches

course book

databasedatabaseoperating systemsoperating systems

DB ConceptsUllmanOS ConceptsShaw

text

We shall see that these two relations are in Fourth Normal Form (4NF)

Multivalued Dependencies (Cont.)Multivalued Dependencies (Cont.)


Multivalued Dependencies (MVDs)Multivalued Dependencies (MVDs)

Let R be a relation schema and let R and R. The multivalued dependency

holds on R if in any legal relation r(R), for all pairs for tuples t1 and t2 in r such that t1[] = t2 [], there exist tuples t3 and t4 in r such that:

t1[] = t2 [] = t3 [] = t4 [] t3[] = t1 [] t3[R – ] = t2[R – ] t4 [] = t2[] t4[R – ] = t1[R – ]


MVD (Cont.)MVD (Cont.)

Tabular representation of


X ->> Y is trivial if

(a) Y X or

(b) Y U X = R

Chapter 7: Relational Database Design

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