Closure and minimum dependency in database

Known relational patterns R（U,F）, among U={ A,B,C,D,E},F It's a collection of relationships {AB—>C,B—>D,C—>E,EC—>B,AC—>B}
seek AB The closure of .

1. First step , set up X0=AB, stay F Find such a relationship in , On the left is AB Subset , That is, on the left A,B,AB, From the title AB—>C,B—>D
2. The second step , take X0 Properties derived from a subset of , Here is C,D And X0 And get up and get X1=ABCD, because X1 It's not equal to X0（ until Xi=Xj） Continue with the calculation
3. Repeat the first step , But be careful at this time , What are you looking for X1 Subset , And it is a subset that has never been used , image A,B,AB There's no need to recalculate , What you should be looking for at this time is C—>E,AC—>B
4. Repeat step 2 , obtain X2=ABCDE, At this time, though X2!=X1, however X2 It contains all the attribute sets , You can also stop and continue the operation , namely AB The closure of is ABCDE

summary ： in other words , When we find a closure of an attribute set , Is to find all the attributes that can be derived directly or indirectly from this attribute , Then continue to merge .

Minimum functional dependency set , First, the following conditions must be met :

1. The right part of a functional dependency can only contain one attribute
2. It does not contain many and dependencies , That is, the set formed after removing a certain functional dependency B And the original set A It is equivalent. , Be frank ,B You can exit the removed functional dependencies
3. Without partial dependency , image F{AB—>C,A—>C} Is not a minimal set of functional dependencies

Known relational patterns R（U,F）, among U={A,B,C},F It's a collection of relationships {A—>BC,B—>C,AB—>C,A—>B}
Find the minimum functional dependency set of the pattern .

answer ：F={B—>C,A—>B},A—>BC The right part of a function dependency cannot contain only one attribute ,B—>C,AB—>C There is a partial dependency ,

It can also be regarded as redundant dependency , because B—>C,AB—>C Is absolutely true , There is no difference between yes and No

--------------------- This article is from legendaryhaha Of CSDN Blog , Full text address please click ：https://blog.csdn.net/legendaryhaha/article/details/80642812?utm_source=copy