5.350. sliding_distribution
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- Origin
- Constraint
- Arguments
- Restrictions
- Purpose
For each sequence of consecutive variables of the collection, each value should be taken by at least and at most variables.
- Example
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The constraint holds since:
On the first sequence of 4 consecutive values values 0, 1, 4, 5 and 6 are respectively used 2, 0, 0, 1 and 1 times.
On the second sequence of 4 consecutive values values 0, 1, 4, 5 and 6 are respectively used 1, 0, 0, 2 and 1 times.
On the third sequence of 4 consecutive values values 0, 1, 4, 5 and 6 are respectively used 2, 0, 0, 1 and 1 times.
On the fourth sequence of 4 consecutive values values 0, 1, 4, 5 and 6 are respectively used 2, 0, 0, 1 and 1 times.
- Typical
- Symmetries
Items of can be reversed.
An occurrence of a value of that does not belong to can be replaced by any other value that also does not belong to .
Items of are permutable.
can be decreased to any value .
can be increased to any value .
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
Contractible wrt. when .
Prefix-contractible wrt. .
Suffix-contractible wrt. .
Contractible wrt. .
- See also
common keyword: , , , Β (sliding sequence constraint).
part of system of constraints: .
specialisation: Β (individual values replaced by single set of values).
- Keywords
characteristic of a constraint: hypergraph.
combinatorial object: sequence.
constraint type: decomposition, sliding sequence constraint, system of constraints.
- Arc input(s)
- Arc generator
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- Arc arity
- Arc constraint(s)
- Graph property(ies)
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- Graph model
Note that the constraint is a constraint where the arc constraints do not have an arity of 2.
PartsΒ (A) andΒ (B) of FigureΒ 5.350.1 respectively show the initial and final graph associated with the Example slot. Since all arc constraints hold (i.e.,Β because of the graph property ) the final graph corresponds to the initial graph.
Figure 5.350.1. (A)Β Initial and (B)Β final graph of the constraint of the Example slot where each ellipse represents an hyperedge involving vertices (to each ellipse corresponds a constraint)