Example 1:
Relation R (ABCDEG) and functional dependencies {AB → C, AC → B, AD → E, B → D, BC → A, E → G}
Decomposition (D) = {AB, BC, ABDE, EG}
Solution:
Let
Let try a search for the first pair of relation which makes lossless join decomposition.
So, it is lossless.
We can join them
Now we have three relations
{ABDE, BC, EG}
Check for joining pair
Now two relations left {ABDEG, BC}
So, the overall decomposition of R (ABCDEG) is lossy decomposition.
Note: We always check one possible best pair not to check all possible pairs.
Example 2:
Let relation R (ABCDEG) and FDs {AB → C, AC → B, AD → E, B → D, BC → A, E → G}
Decomposition D = {ABC, ACDE, ADG}. Find it is lossy or lossless decomposition.
Solution:
Let
Looking for the first pair which is lossless
So, it is a lossless join. Take this pair and join them.
Now two relations left {ABCDE, ADG}
Checking for lossless
So, it is lossless, join them.
So, total decomposition is lossless.
Contributed by