Algorithm # 10 General Algorithm for Testing Loosless Join Decomposition Input: A universal relation R, a decomposition D={R1,R2,...Rm} of R , and a set F of functional dependencies.
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Input: A universal relation R, a decomposition D={R1,R2,...Rm}
of R , and a set F of functional dependencies.
1. Create an initial matrix S with one row for each relation Ri
in D, and one column for each attribute Aj in R.
2. Set S(i,j)= bij for all matrix entries.( Note that each bij is
a distinct symbol associated with indices (i,j) ).
3. For each row i representing relation schema Ri
For each column j representing attribute Aj
IF the relation Ri includes attribute Aj then set S(i,j)= aj.
( Note that aj is a distinct symbol associated with index j)
4. Repeat the following loop until a complete loop execution results in no changes to S
For each functional dependency X→Y in F
For all rows in S that have the same symbols in the columns corresponding to
attributes in X.
Make the symbols in each column that correspond to an
attribute in Y be the same in all these rows as follows:
▪ If any of the rows has an “a” symbol for the column,
set the other rows to that same “a” symbol in the column.
▪If no “a” symbol exists for the attribute in any of the rows,
choose one of the “b” symbols that appears in one of the
rows for the attribute and set the other rows to that same “b”
symbol in the column.
5. If a row made up entirely of “a” symbols, then the decomposition has looless join
property ; otherwise , it does not.
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