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LOSSLESS DECOMPOSITION

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.

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LOSSLESS DECOMPOSITION

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  1. CS157A Lecture 19 LOSSLESS DECOMPOSITION Prof. Sin-Min Lee Department of Computer Science San Jose State University

  2. 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

  3. 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

  4. 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.

  5. 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

  6. A1 A2 A3A4 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)

  7. By FD1: A1 --> A3 A5 we have a new result table A1 A2A3A4A5 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)

  8. 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.

  9. By FD3: A5 --> A1 A4 we have a new result table A1A2A3A4A5 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)

  10. By FD4: A3 A4 --> A2 we get a new result table A1A2A3A4A5 a(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)

  11. 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.

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