Example

Here is an example based on N Associations. The example there is repeated here for reference.

The example has five associated classes: A, C, and E each have one association, B has three associations, and D has two associations:

Pass0: manager multiplier is set to 1, multipliers for each end are set to 1, and initial cardinalities C_i are calculated:

end	AB/A	AB/B	BC/B	BC/C	BD/B	BD/D	DE/D	DE/E
Ci	2	3	2	3	3	5	3	2

Pass 1, step1: For managers that have more than 1 end, a size is calculated for its ends (S_target). Note that managers A, C, and E have just 1 end, and so are not involved in this pass:

manager	calculation	Starget
A
B	LCM(AB/B, BC/B, BD/B) = LCM(3, 2, 3)	6
C
D	LCM(BD/D, DE/D) = LCM(5, 3)	15
E

Pass 1, step2: update multipliers for each end, for each manager (M_i = S_target / C_i):

manager	end	Starget / Ci	Mi
A
B	AB/B	6/3	2
	BC/B	6/2	3
	BD/B	6/3	2
C
D	BD/D	15/5	3
	DE/D	15/3	5
E

Pass 2: If the manager has more than one end, then look at each end, and update manager's multiplier with end's peer's multiplier. In the table below, the change to a manager's multiplier is cumulative, reading down.

manager	end	peer	peer's multiplier	manager's new multiplier
A
B	AB/B	AB/A	1	1
	BC/B	BC/C	1	1
	BD/B	BD/D	3	3
C
D	BD/D	BD/B	2	2
	DE/D	DE/E	1	2
E

Pass 3: If the manager has more than 1 end, it multiplies each end's multiplier by its own multiplier. This reconciles the ends of all managers that are multiply associated.

manager	end	end's multiplier	manager's multiplier	end's new multiplier
A
B	AB/B	2	3	6
	BC/B	3	3	9
	BD/B	2	3	6
C
D	BD/D	3	2	6
	DE/D	5	2	10
E

Pass 4: If the manager has just 1 end, it multiplies the end's multiplier (which is 1 by default) by the end's peer's multiplier. This reconciles the end in all managers with just one association.

manager	end	end's peer	end's new multiplier
A	AB/A	AB/B	6
B
C	BC/C	BC/B	9
D
E	DE/E	DE/D	10

The resulting cardinality, multiplier, and size are shown in the next table. For each pair of ends in an association, the sizes bear the same ratios as the cardinalities. For example, for association AB, the ratio of sizes AB/A:AB/B = 12:18 = 2:3, which is the ratio of the cardinalities for these ends. These sizes also agree with the results from N Associations.

manager	end	cardinality	multiplier	size
A	AB/A	2	6	12
B	AB/B	3	6	18
	BC/B	2	9
	BD/B	3	6
C	BC/C	3	9	27
D	BD/D	5	6	30
	DE/D	3	10
E	DE/E	2	10	20