lossless and dependency preserving methods in DBMS

1. By
Soniya Goyal

2.  It replaces a relation with a collection of
smaller relations.
 It breaks the table into multiple tables in a
database,
 It should always be lossless, because it
confirms that the information in the original
relation cab ne accurately reconstructed
based on the decomposed relations.

3.  There are two types of decomposition
methods:
i) Lossless decomposition
ii) Dependency preserving

4.  Let R be a relation Schema and let f be a set
of functional dependencies on R.
 Let R1 and R2 from a decomposition of R.
R1 ᴧ R2R1
R1 ᴧ R2R2
The attribute common of R1 and R2 must
contain a key for either R1 and R2.

5.  Dependency preserving if every functional
dependency in R can be logically derived from
functional dependencies of R1 and R2 i.e. ,
(F1UF2)+=F+
 Given a relation schema R<S,F> where F is the
associated set of FDs on the attributes in S. R is
decomposed into the relation schemas R1,R2…Rn
with FDs F1,F2,…..Fn. Then this decomposition of R
is dependency preserving if the closure of F`
(where F`=F1UF2U…U Fn) is the identical to F+
(i.e. F`+
=F+)

6.  Let R(A,B,C) and F={AB} then decomposition
of R into R1(A,B) and R2(A,C).
 This decomposition is lossless because the
FD {A B} is contained in R1 and the
common attribute A is a key of R1.

7.  Let R(A,B,C) and F= {AB}.
 Decomposition of R into R1(A,B) and R2(B,C)
is not lossless because the common attribute
B does not functionally determine either A or
C i.e. it is not a key of R1 and R2.

8.  R(A,B,C,D) with the FDs F= {AB, AC,CD},
consider the decomposition of R into
R1(A,B,C) with the FD F1= {AB, AC} and
R2(C,D) with the FD F2= {CD}.
 In this decomposition all the original FDs can
be logically derived from F1 and F2, hence
the decomposition is dependency preserving .
Also the common attribute C form a key of
R2. The decomposition of R into R1 and R2 is
lossless.

9.  Given R(A,B,C,D) with the FDs F= { AB, A
C, AD}
 Decomposition of R into R1(A,B,D) and
R2(B,C) with FDs F1= {AB,AD}, F2={} is
lossy because the common attribute B is not a
candidate key of either R1 or R2.
 The FD AC is not implied by any FDs in R1
or R2 Thus, the decomposition is not
dependency preserving.