5.4. all_differ_from_exactly_k_pos
DESCRIPTION | LINKS | GRAPH |
- Origin
- Constraint
- Type
- Arguments
- Restrictions
- Purpose
Enforce all pairs of distinct vectors of the collection to differ from exactly positions. Enforce when .
- Example
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The constraint holds since:
The first and second vectors differ from 2 positions, which is equal to .
The first and third vectors differ from 2 positions, which is equal to .
The second and third vectors differ from 2 positions, which is equal to .
- Typical
- Symmetries
Items of are permutable.
Items of are permutable (same permutation used).
- Arg. properties
Contractible wrt. .
- See also
implies: Β ( replaced by ), Β ( replaced by ).
- Keywords
characteristic of a constraint: disequality, vector.
- Cond. implications
- Arc input(s)
- Arc generator
-
- 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 5.4.1 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 5.4.1. Initial and final graph of the constraint
(a) (b) - Signature
Since we use the arc generator on the items of the collection, the expression corresponds to the maximum number of arcs of the final graph. Therefore we can rewrite the graph property to . This leads to simplify to .