Denny Tran

CS157B

3/25/2010

Agenda

Definition MVD Rules Examples

Definition

The multivalued dependency X->>Y holds in a relation R if wherever we have two tuples of R that agree in all the attributes of X, then we can swap their Y components and get two new tuples that are also in R.

Graphical Representation

MVD Rules

Every FD is an MVD: If X -> Y, then X ->> Y

A B C1 3 22 1 21 3 32 1 1

A -> B

1: 32: 1

A ->> B

MVD Rules Cont

Complementation: If X ->> Y, then X ->> Z where Z is all attributes not in X or Y.

A B C1 3 22 1 21 3 32 1 1

Show ifA ->> BthenA ->> C

1: 2,32: 2,1

A B C1 32 1

True

Example 1Instructor ->> BookInstructor Book Class

Price Inro Comp MIS 2003Parker Intro Comp MIS 2003Kemp Data in

ActionMIS 4533

Kemp ORACLE Tricks

MIS 4533

Warner Data in Action

MIS 4533

Warner ORACLE Tricks

MIS 4533

Price: Intro CompParker: Intro CompKemp: Data in Action, ORACLE TricksWarner: Data in Action, ORACLE Tricks

Instructor Book Class

Price  Intro Comp MIS 2003

Parker  Intro Comp MIS 2003

Kemp   MIS 4533

Warner   MIS 4533

Data in Action

Data in Action

ORACLE Tricks

ORACLE Tricks

MVD Satisfied!

Example 1 cont

Instructor Book ClassPrice Inro Comp MIS 2003Parker Intro Comp MIS 2003Kemp Data in

ActionMIS 4533

Kemp ORACLE Tricks

MIS 4533

Warner Data in Action

MIS 4533

Warner ORACLE Tricks

MIS 4533

Instructor ->> Class

Price: MIS2003Parker: MIS2003Kemp: MIS4533Warner: MIS4533

Nothing to swap so satisfies MVD.

Example 1 contInstructor Book ClassPrice Inro Comp MIS 2003Parker Intro Comp MIS 2003Kemp Data in

ActionMIS 4533

Kemp ORACLE Tricks

MIS 4533

Warner Data in Action

MIS 4533

Warner ORACLE Tricks

MIS 4533

Class ->> Instructor

MIS2003: Price, ParkerMIS4533: Kemp, Warner

Instructor Book Class  Intro

CompMIS 2003

  Data in Action

MIS 4533

  ORACLE Tricks

MIS 4533

PriceParker

Kemp

Kemp

Warner

Warner

MVD Satisfied!

Example 2Name Area Code Phone Beers

LikedBeer Manufacturer

Sue 650 555-1111 Bud A.B.Sue 650 555-1111 WickedAle Pete'sSue 415 555-9999 Bud A.B.Sue 415 555-9999 WickedAle Pete's

Name ->> Area Code?

Name Area Code Phone Beers Liked

Beer Manufacturer

Sue  415 555-1111 Bud A.B.

Name ->> Phone?

Name Area Code Phone Beers Liked

Beer Manufacturer

Sue 650 555-9999 Bud A.B.

No

No

Example 2 ContName Area Code Phone Beers

LikedBeer Manufacturer

Sue 650 555-1111 Bud A.B.Sue 650 555-1111 WickedAle Pete'sSue 415 555-9999 Bud A.B.Sue 415 555-9999 WickedAle Pete's

Name ->> AreaCode Phone?

Sue: {650, 555-1111}, {415, 555-9999}

Name Area Code Phone Beers Liked

Beer Manufacturer

Sue     Bud A.B.Sue     WickedAle Pete's

Yes!

Example 3: Tuple-generating effect of MVD

A B C D1 1 2 11 2 3 11 3 1 21 2 2 11 3 2 11 1 3 11 3 3 11 1 1 21 2 1 2

1: 1, 2, 3A ->> B

Questions?