Database(9) -- Design Theory

Decomposition:

Recovering Information from a Decomposition

If we do get R back, then we say the decomposition has a lossless join.

• If we decompose a relation according to Algorithm 3.20, then the original relation can be recovered exactly by the natural join.

The Chase Test for Lossless Join

1. The natural join is associative and commutative.
2. Any tuple t in R is surely in π_S1(R) ⨝ π_S2(R) ⨝ … ⨝ π_Sk(R).
3. π_S1(R) ⨝ π_S2(R) ⨝ … ⨝ π_Sk(R) = R when the FD’s in F hold for R if and only if every tuple in the join is also in R.

A	B	C	D
a	b1	c1	d
a	b2	c	d2
a3	b	c	d

Dependency Preservation

We sometimes need to make a tradeoff between preserving dependencies and BNCF.