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Lecture 22. Functional Dependencies (FDs) and Normalization. Schedule Change. http://www.users.csbsju.edu/~irahal/. The Database Design Process. Conceptual design : Use a data model language to come up with an accurate, high-level description of the system requirements

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Lecture 22 l.jpg

Lecture 22

Functional Dependencies (FDs) and


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Schedule Change

  • http://www.users.csbsju.edu/~irahal/

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The Database Design Process

  • Conceptual design:

    • Use a data model language to come up with an accurate, high-level description of the system requirements

    • Words (unstructured)  Diagrams

  • Logical design:

    • Map the resulting EERD into a set of relations

    • Diagram  Relations

  • Physical design:

    • Use DDL on some DBMS to create tables corresponding to your relations

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The Database Design Process

  • Limitations of E-R Designs

    • The EER model provides a set of guidelines

      • Does not result in a unique database schema

    • Does not provide a “formal” way of evaluating alternatives

    • Relies largely on the common sense of the designer

  • Here we try to answer

    • What are the criteria for "good" base relations?

    • Meaningful grouping of attributes

  • When designing a relation schema, how to decide which attributes to include?

    • So far, attributes are grouped to form the relation schema by using the common sense of the database designer

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The Database Design Process

  • First discuss informal guidelines for good relational design

  • Then we discuss formal concepts of functional dependencies and normal forms

    - 1NF (First Normal Form)

    - 2NF (Second Normal Form)

    - 3NF (Third Normal Form)

    - BCNF (Boyce-Codd Normal Form)

  • Additional types of dependencies, further normal forms, relational design algorithms by synthesis are discussed in Chapter 11

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Relation Schema Informal Measures

  • We have some informal measures:

    • Semantics of the attributes

    • Reducing the redundancy values in tuples

    • Disallowing the possibility of generating spurious tuples

    • Reducing null values

  • Not always independent of one another

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Semantics of the Relation Attributes (1)

  • Any grouping of attributes to form a relation schema must portray a certain real-world meaning

  • Each tuple in a relation should represent one entity or relationship instance

  • Guideline 1: Design a relation schema so that it is easy to explain its meaning

    • Semantics of attributes should be easy to interpret

    • Attributes of different entities should not be mixed

    • Only foreign keys should be used to refer to other entities

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Redundant Information (2) from different relations

  • One goal of schema design is to reduce redundancy

    • Information is stored redundantly wasting storage

    • Problems with update anomalies

      • Modification anomalies

      • Insertion anomalies

      • Deletion anomalies

  • Mixing attributes of multiple entities may cause the above problems

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  • Update anomalies from different relations

    • Modification Anomalies

      • Update PNAME from ‘ProductY’ to ‘Customer-Accounting’

    • Insert Anomalies

      • Insert a new employee not assigned to known project

      • Insert a new project with no working employees

    • Delete Project

      • Delete PNUMBER=2

      • Delete the sole employee of a project

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Modification Anomalies from different relations

  • Consider the relation:

    • EMP_PROJ ( Emp#, Proj#, No_hours, Ename, Pname, Plocation)

  • Modification Anomaly:

    • Changing the name of project number P2 from “Project Y” to “Customer-Accounting”

    • May cause this update to be made for all employees working on project P2 otherwise the DB will become inconsistent

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Modification Anomalies from different relations

  • Consider the relation:

    • EMP_PROJ( Emp#, Proj#, No_hours, Ename, Pname, Plocation)

  • Insert Anomaly: Cannot insert a project unless an employee is assigned to

    • Inversely - Cannot insert an employee unless he/she is assigned to a project.

  • Delete Anomaly: When a project is deleted  delete all the employees who work on the project

    • Alternately, if an employee is the sole employee on a project, deleting that employee would result in deleting the corresponding project

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Guidelines to Redundant Information in Tuples and Update Anomalies

  • Guideline 2: Design a schema that does not suffer from the insertion, deletion and update anomalies

  • If there are any present, then note them so that applications can be made to take them into account

    • Might need to break the guidelines to improve performance for certain queries

    • Assume that we always access employee information only with department information

      • The design EMP_PROJ (Emp#, Proj#, No_hours, Ename, Pname, Plocation)might be could for such cases

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SSN Name Address Hobby Anomalies

1111 Joe 123 Main biking

1111 Joe 123 Main hiking




ER Model

SSN Name Address Hobby

1111 Joe 123 Main {biking, hiking}

Relational Model (SSN, Hobby, Name, Address)

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Example Anomalies

  • Redundancy leads to anomalies:

    • A change in Address must be made in several places

    • Suppose a person gives up all hobbies. Do we:

      • Set Hobby attribute to null? No, since Hobby is part of key

      • Delete the entire row? No, since we lose other information in the row

        • No hobby information?

    • Hobby value must be supplied for any inserted row since Hobby is part of key

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Decomposition Anomalies

  • Solution: use two relations to store Person information

    • Person1 (SSN, Name, Address)

    • Hobbies (SSN, Hobby)

  • People with/without hobbies can now be described

  • No update anomalies:

    • Name and address stored once

    • A hobby can be separately supplied or deleted

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Spurious Tuples Anomalies (3)

  • Bad designs for a relational database (or bad decompositions) may result in erroneous results for certain JOIN operations

  • Any decomposition MUST have the "lossless join" property

    • Nospurious tuplesshould be generated by doing a natural-join of any decomposed relations

      • Person1 (SSN, Name, Address)

      • Hobbies (SSN, Name)

    • Here, “loss” relates to loss of information

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Spurious Tuples (3) Anomalies

  • Suppose we replace



  • Guideline 3: The relations should be designed to satisfy the lossless join condition

    • Avoid relations that contain matching attributes that are not (foreign key, primary key) combinations

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Null Values in Tuples Anomalies (4)

  • Guideline 4: Relations should be designed such that their tuples will have as few NULL values as possible

    • Make sure only NULLs are exceptional cases

  • If many attributes do not apply to all tuples in the relation, we end up with many nulls

    • Waste space

    • Ambiguity in meaning

      • Attribute not applicable or invalid

      • Value known to exist, but unavailable

      • Attribute value unknown (may or may not exist)

    • Difficulty specifying JOIN operations (inner or outer joins)

  • Attributes that are NULL frequently could be placed in separate relations (with the primary key)

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Functional Dependencies Anomalies

  • Functional dependencies (FDs) are used to specify formal measures of the "goodness" of a relational database design

  • FDs are constraints that are derived from the meaning and interrelationships of the data attributes

  • An FD is a constraint between two sets of attributes X and Y

    • X  Y holds if whenever two tuples have the same value for X, they must have the same value for Y

    • For any two tuples t1 and t2 in any relation instance r(R):If t1[X]=t2[X], then t1[Y]=t2[Y]

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Functional Dependencies Anomalies

  • X Y: A set of attributes X functionally determines a set of attributes Y (or Y is functionally determined by X) if the value of X determines a unique value for Y

  • X Y in R specifies a constraint on all relation instances r(R)

    • FDs are derived from the real-world constraints on the attributes

    • Property of the intentionof the database

  • An FD is a property of the attributes in the schema R

    • The constraint must hold on every relation instance r(R)

    • Can NEVER be deduced from an extension

      • E.g. if in some case, all people having the same first name are registered for the same course, can we deduce that name  course?

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Examples of FD Constraints Anomalies


  • social security number determines employee name

    • SSN ENAME

  • project number determines project name and location


  • employee SSN and project number determines the hours per week that the employee works on the project


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More on FD Constraints Anomalies

  • Definition of a relation KEY (If K is a key of R)

    • Kfunctionally determines all attributes in R

  • If XY is true, does that make YX true?

  • Some FDs are always true regardless of the relation in which they occur

    • {State, Driver_License_Number}  SSN

    • Zip  {City, State}

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Inference Rules for FDs Anomalies

  • Given a set of FDs F, we can infer additional FDs that hold whenever the FDs in F hold

  • Armstrong's inference rules:

    • IR1. (Reflexive) If Y X, then X Y

      • (Generates trivial FDs)

      • E.g. SSN, ENAME  ENAME

    • IR2. (Augmentation) If X Y, then XZ YZ (Note that XZ stands for X U Z)


    • IR3. (Transitive) If X Y and Y Z, then X Z

      • E.g. SSN DOB and DOB  horoscope sign then SSN  horoscope sign

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Inference Rules for FDs Anomalies

  • IR1, IR2, IR3 form a sound and complete set of inference rules

    • Sound Any rule inferred using IR1, IR2 or IR3 a valid FD

    • Complete  All possible FDs can be generated using them

  • Some additional inference rules that are useful:

    • IR4. (Decomposition) If X YZ, then X Y and X Z

      • SSN  ENAME, DOB then SSN  DOB & SSN  ENAME

    • IR5. (Union) If X Y and X Z, then X YZ

      • SSN  DOB & SSN  ENAME then SSN  ENAME, DOB

    • IR6. (Pseudo-transitivity) If X Y and WY Z, then WX Z

      • Can be deduced from IR1, IR2, and IR3 (completeness property)

      • OfficeLocation Department & Department, Ename  Salary-level then

        OfficeLocation,Ename  Salary-level

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Proofs Anomalies

  • IR1. (Reflexive) If Y X, then X Y

    • For any two tuples t1 and t2 with t1[X] = t2[X] then t1[Y] = t2[Y] because Y X

  • IR2. (Augmentation) If X Y, then XZ YZ

    • Proof by contradiction

      • If for two tuples t1 and t2 we have

        • (1) t1[X] = t2[X]

        • (2) t1[Y] = t2[Y]

        • (3) t1[XZ] = t2[XZ]

        • (4) t1[YZ] ≠ t2[YZ]

      • Can’t be true since from (1) and (3) we have (5) t1[Z] = t2[Z] and from (2) and (5) we have t1[YZ] = t2[YZ] which contradicts (4)

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Proofs Anomalies

  • IR3. (Transitive) If X Y and Y Z, then X Z

    • For any two tuples t1 and t2 with t1[X] = t2[X] then t1[Y] = t2[Y] which implies that t1[Z] = t2[Z] hence X Z holds

  • IR4. (Decomposition) If X YZ, then X Y and X Z

    • X YZ

    • YZ  Y (Using IR1)

    • X  Y (Using IR3)

      • Similarly for X  Z

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Proofs Anomalies

  • IR5. (Union) If X Y and X Z, then X YZ

    • X  Y

    • X  Z

    • X  XY (Using IR1)

    • XY  YZ (Using IR2)

    • X  YZ (Using IR3)

  • IR6. (Psuedotransitivity) If X Y and WY Z, then WX Z

    • X Y

    • WY  Z

    • WX  WY (Using IR2)

    • WX  Z (Using IR3)