# closure - Closure of Attribute Sets Given a set of...

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Closure of Attribute Sets Given a set α of attributes of R and a set of functional dependencies F, we need a way to find all of the attributes of R that are functionally determined by α . This set of attributes is called the closure of α under F and is denoted α +. Finding α + is useful because: if α + = R, then α is a superkey for R if we find α + for all α⊆ R, we've computed F+ (except that we'd need to use decomposition to get all of it). An algorithm for computing α +: result := α repeat temp := result for each functional dependency β γ in F do if β result then result := result γ until temp = result Problem: Compute the closure for relational schema R={A,B,C,D,E} A-->BC CD-->E B-->D E-->A List candidate keys of R. Solution: R={A,B,C,D,E} F, the set of functional dependencies A-->BC, CD-->E, B-->D, E-->A Compute the closure for each β in β γ in F Closure for A Iteration result using 1 A 2 ABC A-->BC 3 ABCD B-->D 4 ABCDE CD-->E 5 ABCDE A+ = ABCDE, Hence A is a super key

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Closure for CD Iteration result using 1
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