Download presentation

Presentation is loading. Please wait.

Published byVance Copas Modified over 2 years ago

1
Chapter 11 Functional Dependencies

2
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.11-2 Topics in this Chapter Basic Definitions Trivial and Nontrivial Dependencies Closure of a Set of Dependencies Closure of a Set of Attributes Irreducible Sets of Dependencies

3
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.11-3 Functional Dependence Functional dependence is a many to one relationship from one set of attributes to another within a given relvar Let r be a relation, and let X and Y be subsets of the attributes of r X Y says “Y is functionally dependent on X”, or “X functionally determines Y” X is the determinant; Y the dependent

4
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.11-4 Trivial and Nontrivial Dependencies An FD is trivial if and only if the right side is a subset of the left side { S#, P# } S# All other dependencies are called nontrivial

5
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.11-5 Closure of a Set of Dependencies The set of all FDs that are implied by a given set S of FDs is called the closure of S Armstrong’s axioms (see next slide) are used to infer FDs from others Let A, B, and C be subsets of relvar R, and let AB signify the union of A and B

6
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.11-6 Closure of a Set of Dependencies – Armstrong’s Axioms Reflexivity: If B is a subset of A the A B Augmentation: If A B, then AC BC Transitivity:If A B and B C, then A C Self-determination: A A Decomposition: If A BC, then A B and A C Union: If A B and A C, then A BC Composition: If A B and C D, then AC BD

7
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.11-7 Closure of a Set of Attributes The set of all attributes that are implied by a given set of attributes S is called the closure of S A superkey implies all the other attributes of a relvar The nonkey attributes of a relvar represent a closure of the superkey, but not necessarily an irreducible one Any group of attributes for which all the other attributes represent a closure is a superkey

8
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.11-8 Irreducible Sets of Dependencies Let S1 and S2 be two sets of FDs. If every FD implied by S1 is implied by S2, then S2 is a cover of S1 A set S of FDs is irreducible iff: The right side of every FD in S involves one attribute (a singleton set) The left side is irreducible No FD in S can be discarded without changing the closure of S

Similar presentations

OK

Chapter 7: Relational Database Design. ©Silberschatz, Korth and Sudarshan7.2Database System Concepts Chapter 7: Relational Database Design First Normal.

Chapter 7: Relational Database Design. ©Silberschatz, Korth and Sudarshan7.2Database System Concepts Chapter 7: Relational Database Design First Normal.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on magic lights Ppt on life history of bill gates Ppt on bodybuilding diet Ppt on trade fair crossword Ppt on historical places in pune india Ppt on quality education quotes Ppt on micro channel heat exchanger Ppt on dc motor speed control using pid Ppt on dynamic web pages Ppt on transportation in human beings higher