Download presentation

Presentation is loading. Please wait.

Published bySidney Cranfield Modified over 2 years ago

1
LOSSLESS DECOMPOSITION Prof. Sin-Min Lee Department of Computer Science San Jose State University

3
Definition of Decomposition A decomposition of a relation R is a set of relations { R1, R2,…, Rn } such that each Ri is a subset of R and the union of all of the Ri is R

4
Example of Decomposition From R( A B C ) we can have two subsets as: R1( A C ) and R2( B C ) if we union R1 and R2 we will get R R = R1 U R2

16
Definition of Lossless Decompotion A decomposition {R1, R2,…, Rn} of a relation R is called a lossless decomposition for R if the natural join of R1, R2,…, Rn produces exactly the relation R.

19
Example R( A1, A2, A3, A4, A5 ) R1( A1, A2, A3, A5 ); R2( A1, A3, A4 ); R3( A4, A5 ) are subsets of R. We have FD1: A1 --> A3 A5 FD2: A2 A3 --> A2 FD3: A5 --> A1 A4 FD4: A3 A4 --> A2

20
A1 A2 A3 A4 A5 a(1) a(2) a(3) b(1,4) a(5) a(1) b(2,2) a(3) a(4) b(2,5) b(3,1) b(3,2) b(3,3) a(4) a(5)

21
By FD1: A1 --> A3 A5 we have a new result table A1 A2 A3 A4 A5 a(1) a(2) a(3) b(1,4) a(5) a(1) b(2,2) a(3) a(4) a(5) b(3,1) b(3,2) b(3,3) a(4) a(5)

22
By FD2: A2 A3 --> A4 we don’t have a new result table because we don’t have any equally elements. Therefore, the result doesn’t change.

23
By FD3: A5 --> A1 A4 we have a new result table A1 A2 A3 A4 A5 a(1) a(2) a(3) a(4) a(5) a(1) b(2,2) a(3) a(4) a(5) b(3,1) b(3,2) b(3,3) a(4) a(5)

24
By FD4: A3 A4 --> A2 we get a new result table A1 A2 A3 A4 A5 a(1) a(2) a(3) a(4) a(5) b(3,1) b(3,2) b(3,3) a(4) a(5) tuple1 and tuple2 are lossless because they have all a(I)

25
Summary A decomposition { R1, R2,…, Rn } of a relation R is called a lossless decomposition for R if the natural join of R1, R2,…, Rn produces exactly the relation R NOTE: not every decomposition is lossless. It is possible to produce a decomposition that is lossy, one that losses information.

Similar presentations

OK

Functional Dependencies An example: loan-info= Observe: tuples with the same value for lno will always have the same value for amt We write: lno amt.

Functional Dependencies An example: loan-info= Observe: tuples with the same value for lno will always have the same value for amt We write: lno amt.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on the solar system Ppt on computer malwares anti Ppt on mass media and society Ppt on gsm based home automation system Ppt on cost accounting standard A ppt on loch ness monster south Ppt on online railway reservation system Ppt on power sharing in india download song Ppt on asian continent videos Ppt on potential reuse of plastic waste in road construction