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  • Basics of FDs
  • Manipulating FDs
  • Closures and Keys
  • Minimal Bases

Functional Dependencies

T. M. Murali
October 19, 21 2009

  • T. M. Murali
  • October 19, 21 2009
  • CS 4604: Functional Dependencies

Basics of FDs

  • Manipulating FDs
  • Closures and Keys
  • Minimal Bases

Example

  • Name
  • Id

Name
Id

  • Advises
  • Advisors

Students

Favourite

I

Convert to relations:

  • T. M. Murali
  • October 19, 21 2009
  • CS 4604: Functional Dependencies

Basics of FDs

  • Manipulating FDs
  • Closures and Keys
  • Minimal Bases

Example

  • Name
  • Id

Name
Id

  • Advises
  • Advisors

Students

Favourite

I

Convert to relations:

Students(Id, Name) Advisors(Id, Name) Advises(StudentId, AdvisorId) Favourite(StudentId, AdvisorId)

  • T. M. Murali
  • October 19, 21 2009
  • CS 4604: Functional Dependencies

Basics of FDs

  • Manipulating FDs
  • Closures and Keys
  • Minimal Bases

Example

  • Name
  • Id

Name
Id

  • Advises
  • Advisors

Students

Favourite

II

Convert to relations:

Students(Id, Name) Advisors(Id, Name) Advises(StudentId, AdvisorId) Favourite(StudentId, AdvisorId)

Suppose we perversely decide to convert Students, Advises, and Favourite into one relation.

Students(Id, Name, AdvisorId, AdvisorName, FavouriteAdvisorId)

  • T. M. Murali
  • October 19, 21 2009
  • CS 4604: Functional Dependencies

Basics of FDs

  • Manipulating FDs
  • Closures and Keys
  • Minimal Bases

Example of a Bad Relation

Students(Id, Name, AdvisorId, AdvisorName, FavouriteAdvisorId)

I

If you know a student’s Id, can you determine the values of any other attributes?

  • T. M. Murali
  • October 19, 21 2009
  • CS 4604: Functional Dependencies

Basics of FDs

  • Manipulating FDs
  • Closures and Keys
  • Minimal Bases

Example of a Bad Relation

Students(Id, Name, AdvisorId, AdvisorName, FavouriteAdvisorId)

I

If you know a student’s Id, can you determine the values of any other

attributes? Name and FavouriteAdvisorId.

  • T. M. Murali
  • October 19, 21 2009
  • CS 4604: Functional Dependencies

Basics of FDs

  • Manipulating FDs
  • Closures and Keys
  • Minimal Bases

Example of a Bad Relation

Students(Id, Name, AdvisorId, AdvisorName, FavouriteAdvisorId)

I

If you know a student’s Id, can you determine the values of any other

attributes? Name and FavouriteAdvisorId.

Id → Name Id → FavouriteAdvisorId

  • T. M. Murali
  • October 19, 21 2009
  • CS 4604: Functional Dependencies

Basics of FDs

  • Manipulating FDs
  • Closures and Keys
  • Minimal Bases

Example of a Bad Relation

Students(Id, Name, AdvisorId, AdvisorName, FavouriteAdvisorId)

I

If you know a student’s Id, can you determine the values of any other

attributes? Name and FavouriteAdvisorId.

Id → Name Id → FavouriteAdvisorId AdvisorId →

  • T. M. Murali
  • October 19, 21 2009
  • CS 4604: Functional Dependencies

Basics of FDs

  • Manipulating FDs
  • Closures and Keys
  • Minimal Bases

Example of a Bad Relation

Students(Id, Name, AdvisorId, AdvisorName, FavouriteAdvisorId)

I

If you know a student’s Id, can you determine the values of any other

attributes? Name and FavouriteAdvisorId.

Id → Name Id → FavouriteAdvisorId AdvisorId → AdvisorName

  • T. M. Murali
  • October 19, 21 2009
  • CS 4604: Functional Dependencies

Basics of FDs

  • Manipulating FDs
  • Closures and Keys
  • Minimal Bases

Example of a Bad Relation

Students(Id, Name, AdvisorId, AdvisorName, FavouriteAdvisorId)

II

If you know a student’s Id, can you determine the values of any other

attributes? Name and FavouriteAdvisorId.

Id → Name Id → FavouriteAdvisorId AdvisorId → AdvisorName

Can we say Id → AdvisorId?

  • T. M. Murali
  • October 19, 21 2009
  • CS 4604: Functional Dependencies

Basics of FDs

  • Manipulating FDs
  • Closures and Keys
  • Minimal Bases

Example of a Bad Relation

Students(Id, Name, AdvisorId, AdvisorName, FavouriteAdvisorId)

II

If you know a student’s Id, can you determine the values of any other

attributes? Name and FavouriteAdvisorId.

Id → Name Id → FavouriteAdvisorId AdvisorId → AdvisorName

Can we say Id → AdvisorId? NO! Id is not a key for the Students relation.

  • T. M. Murali
  • October 19, 21 2009
  • CS 4604: Functional Dependencies

Basics of FDs

  • Manipulating FDs
  • Closures and Keys
  • Minimal Bases

Example of a Bad Relation

Students(Id, Name, AdvisorId, AdvisorName, FavouriteAdvisorId)

I

If you know a student’s Id, can you determine the values of any other

attributes? Name and FavouriteAdvisorId.

Id → Name Id → FavouriteAdvisorId AdvisorId → AdvisorName

II

Can we say Id → AdvisorId? NO! Id is not a key for the Students relation. What is the key for the Students?

  • T. M. Murali
  • October 19, 21 2009
  • CS 4604: Functional Dependencies

Basics of FDs

  • Manipulating FDs
  • Closures and Keys
  • Minimal Bases

Example of a Bad Relation

Students(Id, Name, AdvisorId, AdvisorName, FavouriteAdvisorId)

I

If you know a student’s Id, can you determine the values of any other

attributes? Name and FavouriteAdvisorId.

Id → Name Id → FavouriteAdvisorId AdvisorId → AdvisorName

II

Can we say Id → AdvisorId? NO! Id is not a key for the Students relation. What is the key for the Students? {Id, AdvisorId}.

  • T. M. Murali
  • October 19, 21 2009
  • CS 4604: Functional Dependencies

Basics of FDs

  • Manipulating FDs
  • Closures and Keys
  • Minimal Bases

Example of a Bad Relation

Students(Id, Name, AdvisorId, AdvisorName, FavouriteAdvisorId)

II

If you know a student’s Id, can you determine the values of any other

attributes? Name and FavouriteAdvisorId.

Id → Name Id → FavouriteAdvisorId AdvisorId → AdvisorName

Can we say Id → AdvisorId? NO! Id is not a key for the Students relation.

II

What is the key for the Students? {Id, AdvisorId}. Why is this relation“bad?”

  • T. M. Murali
  • October 19, 21 2009
  • CS 4604: Functional Dependencies

Basics of FDs

  • Manipulating FDs
  • Closures and Keys
  • Minimal Bases

Example of a Bad Relation

Students(Id, Name, AdvisorId, AdvisorName, FavouriteAdvisorId)

II

If you know a student’s Id, can you determine the values of any other

attributes? Name and FavouriteAdvisorId.

Id → Name Id → FavouriteAdvisorId AdvisorId → AdvisorName

Can we say Id → AdvisorId? NO! Id is not a key for the Students relation.

II

What is the key for the Students? {Id, AdvisorId}. Why is this relation“bad?” Parts of the key determine other attributes.

  • T. M. Murali
  • October 19, 21 2009
  • CS 4604: Functional Dependencies

Basics of FDs

  • Manipulating FDs
  • Closures and Keys
  • Minimal Bases

Motivation for Functional Dependencies

IIII

Reason about constraints on attributes in a relation. Procedurally determine the keys of a relation. Detect when a relation has redundant information. Improve database designs systematically using normalisation.

  • T. M. Murali
  • October 19, 21 2009
  • CS 4604: Functional Dependencies

Basics of FDs

  • Manipulating FDs
  • Closures and Keys
  • Minimal Bases

Definition of Functional Dependency

I

If t is a tuple in a relation R and A is an attribute of R, then tA is the value of attribute A in tuple t.

  • T. M. Murali
  • October 19, 21 2009
  • CS 4604: Functional Dependencies

Basics of FDs

  • Manipulating FDs
  • Closures and Keys
  • Minimal Bases

Definition of Functional Dependency

II

If t is a tuple in a relation R and A is an attribute of R, then tA is the value of attribute A in tuple t. The FD AdvisorId → AdvisorName holds in R if in every instance of R, for every pair of tuples t and u

  • T. M. Murali
  • October 19, 21 2009
  • CS 4604: Functional Dependencies

Basics of FDs

  • Manipulating FDs
  • Closures and Keys
  • Minimal Bases

Definition of Functional Dependency

II

If t is a tuple in a relation R and A is an attribute of R, then tA is the value of attribute A in tuple t. The FD AdvisorId → AdvisorName holds in R if in every instance of R, for every pair of tuples t and u

if tAdvisorId = uAdvisorId, then tAdvisorName = uAdvisorName

.

  • T. M. Murali
  • October 19, 21 2009
  • CS 4604: Functional Dependencies

Basics of FDs

  • Manipulating FDs
  • Closures and Keys
  • Minimal Bases

Definition of Functional Dependencies

A functional dependency (FD) on a relation R is a statement

I

If two tuples in R agree on attributes A1, A2, . . . An then they agree on attribute B.

I

Notation: A1A2 . . . An → B

  • T. M. Murali
  • October 19, 21 2009
  • CS 4604: Functional Dependencies

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  • Functional Dependency and Normalization for Relational Databases

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  • Chapter 4: Functional Dependencies

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  • Functional Dependencies and Normalization

    Functional Dependencies and Normalization

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  • A Survey of Database Dependency Concepts

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    A Survey of Database Dependency Concepts Nikita Bobrov Anastasia Birillo George Chernishev Saint Petersburg State University Saint Petersburg State University Saint Petersburg State University, Email: [email protected] Email: [email protected] JetBrains Research Email: [email protected] Abstract—A database dependency is a formal concept which sub-types were proposed. Currently, there is a dozen of major is used to describe patterns in data. These patterns are employed dependency types. during data analysis, data cleansing, and schema normalization. In this paper we survey database dependency concepts There is about dozen of major dependency types. In this paper we survey these types of database dependencies employed in the relational databases. We survey them starting employed in the relational databases. We start from the earliest from the earliest ones and conclude with the state-of-the-art ones — functional dependencies and conclude with the state-of- findings. We provide both formal and non-formal definitions the-art findings. For each type we provide both formal and non- and present an example for each type. We also briefly discuss formal definitions and present an example and counterexample. extraction algorithms and possible use cases. Our goal is to We also briefly discuss extraction algorithms and possible use cases. produce a broad survey that involves major types of database dependencies without delving into details. I. INTRODUCTION II. MOTIVATION The era of big data not only presents new opportunities, but also poses new challenges for both industry and academy. The The idea of this paper arrived during our development of a challenges come from the three “Vs”, which are frequently data-driven tool for automatic database physical design.