无损连接分解和有损连接分解的区别

将关系分解为更小的子关系的过程称为分解。 DBMS 需要分解来将关系转换为特定的范式，这进一步减少了关系中的冗余、异常和不一致。

DBMS 中主要有两种类型的分解——

1. 无损分解
2. 有损分解

无损和有损连接分解的区别：

Lossless	Lossy
The decompositions R1, R2, R2…Rn for a relation schema R are said to be Lossless if there natural join results the original relation R.	The decompositions R1, R2, R2…Rn for a relation schema R are said to be Lossy if there natural join results into additon of extraneous tuples with the the original relation R.
Formally, Let R be a relation and R1, R2, R3 … Rn be it’s decomposition, the decomposition is lossless if –	Formally, Let R be a relation and R1, R2, R3 … Rn be it’s decomposition, the decomposition is lossy if –
There is no loss of information as the relation obtained after natural join of decompositions is equivalent to original relation.Thus, it is also referred to as non-additive join decomposition	There is loss of information as extraneous tuples are added into the relation after natural join of decompositions. Thus, it is also referred to as careless decomposition.
The common attribute of the sub relations is a superkey of any one of the relation.	The common attribute of the sub relation is not a superkey of any of the sub relation.

示例 1：
示例检查是否给定的 Decomposition Lossless Join Decomposition。

假设有一个关系模式 R(A, B, C)。 R1(A, B) 和 R2(B, C) 是它的分解。

R

A	B	C
a1	b1	c1
a2	b1	c1
a1	b2	c2

R1

A	B
a1	b1
a2	b1
a1	b2

R2

B	C
b1	c1
b1	c1
b2	c2

现在为了分解是无损的，

R1 ⨝ R2 ⨝ R3 .... ⨝ Rn = R

R1 ⨝ R2

A	B	C
a1	b1	c1
a2	b1	c1
a1	b2	c2

R ⊂ R1 ⨝ R2 ⨝ R3 .... ⨝ Rn

这种分解是无损的。

示例 2：
示例检查是否给定的 Decomposition Lossy Join Decomposition。

假设有一个关系模式 R(A, B, C)。 R1(A, B) 和 R2(A, C) 是它的分解。

R

A	B	C
a1	b1	c1
a2	b1	c1
a1	b2	c2
a1	b3	c3

R1

A	B
a1	b1
a2	b1
a1	b2
a1	b3

R2

A	C
a1	c1
a2	c1
a1	c2
a1	c3

现在分解是有损的，

R1 ⨝ R2 = R then, R1 ⨝ R2  is

R1 ⨝ R2

A	B	C
a1	b1	c1
a1	b1	c2
a2	b1	c1
a1	b2	c2
a1	b2	c1
a1	b3	c3
a1	b3	c1

As, R1 ⨝ R2 = R, 

这种分解是有损的。

因此，我们可以确定分解是无损的还是有损的。