5.22. allperm
| DESCRIPTION | LINKS | GRAPH |
- Origin
- Constraint
- Synonyms
, .
- Type
- Argument
- Restrictions
- Purpose
Given a matrix of domain variables, enforces that the first row is lexicographically less than or equal to all permutations of all other rows. Note that the components of a given vector of the matrix may be equal.
- Example
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The constraint holds since vector is lexicographically less than or equal to all the permutations of vector (i.e.,Β , , , , , ).
- Typical
- Symmetry
One and the same constant can be added to the attribute of all items of .
- Arg. properties
Suffix-contractible wrt. (remove items from same position).
- Usage
A symmetry-breaking constraint.
- See also
common keyword: , Β (matrix symmetry,lexicographic order), Β (lexicographic order), Β (matrix symmetry,lexicographic order), Β (lexicographic order).
- Keywords
characteristic of a constraint: sort based reformulation, vector.
constraint type: order constraint, system of constraints.
final graph structure: acyclic, bipartite.
- Arc input(s)
- Arc generator
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- Arc arity
- Arc constraint(s)
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- Graph property(ies)
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- Graph class
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- Graph model
We generate a graph with an arc constraint between the vertex corresponding to the first item of the collection and the vertices associated with all other items of the collection. This is achieved by specifying that (1)Β an arc should start from the first item (i.e.,Β ) and (2)Β an arc should not end on the first item (i.e.,Β ). We finally state that all these arcs should belong to the final graph. PartsΒ (A) andΒ (B) of FigureΒ 5.22.1 respectively show the initial and final graph associated with the Example slot.
Figure 5.22.1. Initial and final graph of the constraint
(a) (b)