5.10. all_incomparable
DESCRIPTION | LINKS | GRAPH |
- Origin
Inspired by incomparable rectangles.
- Constraint
- Synonym
.
- Type
- Argument
- Restrictions
- Purpose
Enforce for each pair of distinct vectors of the collection the fact that they are incomparable. Two vectors and are incomparable if and only, when the components of both vectors are ordered, and respectively denoted by and , we neither have (for all ) nor have (for all ).
- Example
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The constraint holds since all distinct pairs of vectors are incomparable as illustrated by FigureΒ 5.10.1.
Figure 5.10.1. Illustrating the incomparability of vectors , , , , , , : first to each vector we associate a rectangle whose sizes are the components of the vector; second no matter whether we rotate a rectangle from or not, one rectangle can not be included in another rectangle.
- All solutions
FigureΒ 5.10.2 gives all solutions to the following non ground instance of the constraint: , , , , , , .
Figure 5.10.2. All solutions corresponding to the non ground example of the constraint of the All solutions slot
- Typical
- Symmetry
Items of are permutable.
- Arg. properties
Contractible wrt. .
- See also
implies: .
- Keywords
characteristic of a constraint: vector.
- Cond. implications
- Arc input(s)
- Arc generator
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- Arc arity
- Arc constraint(s)
- Graph property(ies)
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- Graph class
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- Graph model
The Arc constraint(s) slot uses the constraint defined in this catalogue.
PartsΒ (A) andΒ (B) of FigureΒ 5.10.3 respectively show the initial and final graph associated with the Example slot. Since we use the graph property, the arcs of the final graph are stressed in bold. The previous constraint holds since exactly arc constraints hold.
Figure 5.10.3. Initial and final graph of the constraint
(a) (b)