5.219. lex2
| DESCRIPTION | LINKS |
- Origin
- Constraint
- Synonyms
, .
- Type
- Argument
- Restrictions
- Purpose
Given a matrix of domain variables, enforces that both adjacent rows, and adjacent columns are lexicographically ordered (adjacent rows and adjacent columns can be equal).
- Example
-
The constraint holds since:
The first row is lexicographically less than or equal to the second row .
The first column is lexicographically less than or equal to the second column .
The second column is lexicographically less than or equal to the third column .
- Typical
- Symmetry
One and the same constant can be added to the attribute of all items of .
- Usage
A symmetry-breaking constraint.
- Remark
The idea of this symmetry-breaking constraint can already be found in the following articles of A.Β LubiwΒ [Lubiw85], [Lubiw87].
In block designs you sometimes want repeated blocks, so using the non-strict order would be required in this case.
- Reformulation
The constraint can be expressed as a conjunction of two constraints: A first constraint on the argument and a second constraint on the transpose of the argument.
- Systems
- See also
common keyword: , Β (matrix symmetry,lexicographic order).
implies: .
- Keywords
constraint type: predefined constraint, system of constraints, order constraint.