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Examples of Lossless Join Decomposition

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.

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Contributed by

Debashis Roy Faculty of Computer Science Department, JCC College, University of Calcutta