5.388. sum_of_weights_of_distinct_values
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- Origin
- Constraint
- Synonym
.
- Arguments
- Restrictions
- Purpose
All variables of the collection take a value in the collection. In addition is the sum of the attributes associated with the distinct values taken by the variables of .
- Example
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The constraint holds since its last argument is equal to the sum of the weights of the values 1 and 6 that occur within the collection.
- Typical
- Symmetries
Items of are permutable.
All occurrences of two distinct values of can be swapped.
Items of are permutable.
All occurrences of two distinct values in or can be swapped; all occurrences of a value in or can be renamed to any unused value.
- Arg. properties
Functional dependency: determined by and .
- See also
attached to cost variant: Β (all values have a weight of 1).
common keyword: , , Β (weighted assignment).
- Keywords
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constraint arguments: pure functional dependency.
filtering: cost filtering constraint.
modelling: functional dependency.
problems: domination, weighted assignment, facilities location problem.
- Arc input(s)
- Arc generator
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- Arc arity
- Arc constraint(s)
- Graph property(ies)
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- Signature
Since we use the arc generator, the number of sources of the final graph cannot exceed the number of sources of the initial graph. Since the initial graph contains sources, this number is an upper bound of the number of sources of the final graph. Therefore we can rewrite to and simplify to .
PartsΒ (A) andΒ (B) of FigureΒ 5.388.1 respectively show the initial and final graph associated with the Example slot. Since we use the graph property, the source vertices of the final graph are shown in a double circle. Since we also use the graph property we show the vertices from which we compute the total cost in a box.
Figure 5.388.1. Initial and final graph of the constraint
(a) (b)