5.309. ordered_nvector
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- Origin
- Constraint
- Synonyms
, , .
- Type
- Arguments
- Restrictions
- Purpose
Enforces the following two conditions:
is the number of distinct tuples of values assigned to the vectors of the collection . Two tuples of values and are if and only if there exist an integer such that .
For each pair of consecutive vectors and of the collection we have that is lexicographically less than or equal to . Given two vectors, and of components, and , is lexicographically less than or equal to if and only if or or and is lexicographically less than or equal to .
- Example
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The constraint holds since:
Its first argument is set to the number of distinct tuples of values (i.e.,Β tuples and ) occurring within the collection .
The vectors of the collection are sorted in increasing lexicographical order.
- Typical
- Arg. properties
Functional dependency: determined by .
Contractible wrt. when and .
Contractible wrt. when .
- Reformulation
The constraint can be reformulated as a conjunction of a and a constraints.
- See also
implies: Β ( of constraint removed), , Β ( replaced by ), Β ( replaced by ).
related: .
- Keywords
characteristic of a constraint: vector.
constraint type: counting constraint, order constraint.
- Arc input(s)
- Arc generator
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- Arc arity
- Arc constraint(s)
- Graph property(ies)
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- Arc input(s)
- Arc generator
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- Arc arity
- Arc constraint(s)
- Graph property(ies)
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- Graph model
PartsΒ (A) andΒ (B) of FigureΒ 5.309.1 respectively show the initial and final graph of the second graph constraint associated with the Example slot. Since we use the graph property in this second graph constraint, we show the different connected components of the final graph. Each strongly connected component corresponds to a tuple of values that is assigned to some vectors of the collection. The 2 following tuple of values and are used by the vectors of the collection.
Figure 5.309.1. Initial and final graph of the constraint
(a) (b)