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composes a new relation which combines the data elements The join operation from two relations A join can be de ned as a cartesian product of two relations followed by a selection creating a subset (Eqs 7-21 and 7-24) The subset consists of those tuples which have identical or matching values for the join attribute A join is su ciently important and frequent that it warrants its own de nition Each relation R1 , R2 being joined will have a join attribute J To permit the comparison the attributes Ri J have to be compatible, just as the entire relationschemas had to be compatible for the set operations (Eq 7-17) R9 (S9 , T9 ) = R1 (S1 , T1 ) giving
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J1 J2
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S 9 = S1 & S 2 so that each tuple t T9 = t1 T1 &t2 T2 , t1 J1 t2 J2 Then 0 n9 n1 n2 and a9 = a1 + a2
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The extract function used is as de ned in Eq 7-22, but may be extended to include cases where J consists of multiple attributes In our program examples we specify a join based on an equal comparison ( = "=") as follows:
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All attributes of the two relations are included in the resulting tuples We note that if a tuple matches multiple entries in the other relation, multiple tuples are placed into the result, and if several entries in both relations match each other, their cartesian product appears in the join The join comes in various avors The most common join is the equi-join shown, with = "=" Here all result tuples are formed by combining input tuples which have identical values in the attribute columns identi ed by J The columns from the two relations involved in the equi-join are equal and one set can be omitted from the result relation, making this a natural join If the number of attributes in J is j, the relation-schema for a natural join R9 = R1 R2 will be
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J1 =J2
S9 = S1 &S2 J a9 = a1 + a2 j
7-26
The equi-join is the join intended when no further speci cations are given A symbolic presentation of a join is shown in Fig 7-22 Joins are also implemented which use for r1 j =, >, < r2 j Conceptually arbitrary functions might be used for , so that the constraint of compatible domains for J might be relaxed Such extensions have not been explored The implementation of a join rarely follows the steps implied by the de nition Generation of the cartesion product is avoided A simple scheme is the inner-outerloop join For each tuple in R1 all tuples of R2 are inspected and if the condition R1 J R2 J is true an output tuple is constructed Other and better methods will be found in Sec 9-3-3 Parts skill required:
assembly, 750381 750381 750381 750381 750381 type, Body Body Body Fender Fender p id P1 P2 P4 P1 P3
RELATION
no req, 10 12 22 26 26
skill req Machinist Machinist Welder Machinist Welder
Supply:
s id,
RELATION
p id
quantity
see Fig 7-16 Parts assembly:
assembly, 750381 750381 750381 750381 750381 750381 750381 type, Body Body Body Body Fender Fender Fender
RELATION = Parts skill requiredp id
p id, P1 P2 P4 P4 P1 P3 P3 s id : S1 S2 S2 S4 S1 S1 S2 no req, 10 12 22 22 26 26 26 skill req, Machinist Machinist Welder Welder Machinist Welder Welder
Supplyp id
#7; 160 140 90 100 160 60 50
Figure 7-23
Natural join
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A natural join is shown in Fig 7-23 The join attribute is called p id in both relations and the domain is obviously identical While deleting the redundant join attribute we will rearrange the attributes in accordance with our ruling : dependent part conventions
Computed Join In Eq 7-25 we de ned the join for an arbitrary computation A sample join operation, based on a complex comparison, which uses the same relations is shown in Fig 7-24 The objective is to obtain a list of production combinations for which the part Supplyp id in stock is less than ten times the assembly,type requirement
Supply:
RELATION see Fig 7-16 RELATION see Fig 7-23 Supply RELATION = Parts skill required Parts skill requiredp id = Supplyp id, Parts skill requiredno req * 10 > Supplyquantity;
type, Body Body Fender Fender Fender p id, P4 P4 P1 P3 P3 no req, 22 22 26 26 26 skill req, Welder Welder Machinist Welder Welder s id, S2 S4 S1 S1 S2 p id', P4 P4 P1 P3 P3 quantity ; 90 100 160 60 50
Parts skill required: Low stock:
assembly, 750381 750381 750381 750381 750381
Figure 7-24
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