lossless decomposition
DESCRIPTION
CS157A Lecture 19. LOSSLESS DECOMPOSITION. Prof. Sin-Min Lee Department of Computer Science San Jose State University. 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. - PowerPoint PPT PresentationTRANSCRIPT
LOSSLESS DECOMPOSITION
Prof. Sin-Min LeeDepartment of Computer Science
San Jose State University
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
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 RR = R1 U R2
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.
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
A1 A2 A3 A4 A5a(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)
By FD1: A1 --> A3 A5we have a new result table
A1 A2 A3 A4 A5a(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)
By FD2: A2 A3 --> A4we don’t have a new result table because we
don’t have any equally elements. Therefore, the result doesn’t change.
By FD3: A5 --> A1 A4
we have a new result tableA1 A2 A3 A4 A5a(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)
By FD4: A3 A4 --> A2we get a new result tableA1 A2 A3 A4 A5a(1) a(2) a(3) a(4) a(5)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)
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.