1 Term 2, 2004, Lecture 2, Normalisation - IntroductionMarian Ursu, Department of Computing,...

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Term 2, 2004, Lecture 2, Normalisation - Introduction Marian Ursu, Department of Computing, Goldsmiths College

NormalisationIntroduction

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Outline

motivation: • database design – validation

• redundancy / update anomalies

basis: functional dependencies (FDs)• definitions

• examples

• concepts and terminology

• semantic assumtpions

• (more) advanced theoretical issues (in brief)

normal form: illustration• definition

• example

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Database Design

relational model how do we know whether a relational model is good or not? how do we know whether a relation is well designed or not?

normal forms a (semi-)formal way of validating a relational model, from the

point of view of reducing the redundancy of data

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Redundancy

Student-Modules

S_id S_name P_ tutor Module Val Res

50021 G. Zolla MFU Database Systems 1cu A

50021 G. Zolla MFU Software Engineering 1cu null

50021 G. Zolla MFU Advanced Programming 1/2cu B

50012 D. Petrescu MFU Computing 1cu null

50012 D. Petrescu MFU Mathematics 1/2cu A

41002 T.A. Flo MFU HCI 1/2cu null

50033 D. Wise MH Database Systems 1cu null

50033 D. Wise MH Algorithms 1cu null

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Redundancy










Student-Modules

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Redundancy

a relation contains redundant data if it stores the same information more than once

a relational model may have redundancy and at the same time have no redundant relations how? give an example

redundant data may cause update anomalies and may lead to inconsistencies

normalisation deals with redundant data at the level of individual relations

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Update anomalies - insertion

insert the fact that 50012 takes “Networks - Introduction”; the name of the student and the name of the personal tutor have to be entered as well; this is prone to errors inconsistent data

the structure of the relation does not prevent such errors from happening

can you identify other kinds of update anomalies on this relation?





50012 D. Pwtrwscu MFFU Networks 1/2cu null


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Update anomalies - deletion

delete the fact that 41002 takes “HCI”, in the original table; relevant information will be also deleted - about “T.A Flo” and about “HCI”











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Update anomalies - modification

it is possible to modify an attribute and to bring the relation in an inconsistent state; e.g. it is possible (e.g. by mistake) to modify the value of “Database Systems” to “1/2cu” in just some rows; such situations must be avoided



50021 G. Zolla MFU Database Systems 1/2cu A





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Update anomalies

update anomalies may lead to inconsistent data are caused by redundancy

normal forms are a “measure” of the amount of redundancy in a relation are defined on the basis of a simpler concept:

functional dependencies

normalisation a way of transforming relations to eliminate redundancies no data should be lost/changed through normalisation

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Functional dependency (FD)

R - relation, X and Y - subsets of attributes of R

X Y iff

in every possible legal value of R each X-value has a single Y-value associated

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Examples

S_id S_nameS_id P_TutorS_id S_id(S_id, S_name) P_tutor(S_id, S_name, P_tutor) P_tutorModule Val(S_id, Module) Res(S_id, S_name, P_tutor, Module, Val) Res

(S_id, S_name, P_tutor, Module, Val, Res)

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Concepts

FD is a semantic concept• you must understand the meaning of the attributes

determinant / dependent trivial / non-trivial left-irreducible

• yes: (S_id, S_name) P_tutor

• no: (S_id, Module) Res

closure irreducible set

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Semantic assumptions

FDs are “deduced” from the semantic assumptions (that define the application) (patient, symptom, doctor, practice, diagnosis) a patient is seen only by one doctor

• patient doctor

a patient, for a given symptom, is seen by only one doctor• patient, symptom doctor

a doctor gives only one diagnosis for a symptom of one patient

• patient, symptom, doctor diagnosis

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Operations with FDs

inference rules augmentation: if AB then ACBC transitivity : if A B and BC then AC decomposition: if ABC then AB and AC union: if AB and AC then ABC composition: if AB and CD then ACBD

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Functional diagram

S_id

City

P_tutor

S_name

S_id

ModuleRes

Module

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FDs and Keys

define a candidate key (CK) in terms of FDs how is a FD expressed in a relation?

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Closure

all FDs that can be derived from a given set S• notation S+

Armstrong’s inference rules• for a partial set refer to slide “Operations with FDs”

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Irreducible set

S1 covers S2 iff S2+ S1

+

S is irreducible iff• RightHandSide of every FD is non-composite• all FDs in S are left-irreducible• no FD ca be discarded from S without changing S+

a database that enforces S enforces, in fact, S+

the irreducible set of S is S’ iff• S’ - irreducible• S’+ = S+

more efficient to work with the irreducible set

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1NF – First Normal Form

not based on FDs a relation is in 1NF if and only if all the domains of its

attributes contain only scalar values the relational model can only contain relations in 1NF

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2NF – Second Normal Form

a relation (with just one CK) is in 2NF if and only if it is in 1NF and there is no FD from a subset of attributes of the PK to a non-key attribute

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2NF – Examples

not 2NF (S_id, S_name, S_add, M_id, M_name, M_type, M_val, Result) why?

2NF (S_id, S_name, S_add) (M_id, M_name, M_type, M_val) (S_id, M_id, Result)

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3NF – Third Normal Form

a relation (with just one CK) is in 3NF if and only if it is in 2NF and there is no FD between non-key attributes

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3NF - Examples

not 3NF (M_id, M_name, M_type, M_val) why?

3NF (M_id, M_name, M_type) (M_type, M_val)

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Normalisation

the process of transforming a relation with redundancies into an “equivalent” set of relations that have less redundancies equivalent – non-loss decomposition

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Conclusion

redundancy update anomalies normal forms – solution functional dependencies normal forms – simple definitions and examples

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1 Term 2, 2004, Lecture 2, Normalisation - IntroductionMarian Ursu, Department of Computing,...

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