5.113. domain

DESCRIPTIONLINKS
Origin

Domain definition.

Constraint

πšπš˜πš–πšŠπš’πš—(πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚,π™»π™Ύπš†,πš„π™Ώ)

Synonym

πšπš˜πš–.

Arguments
πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚πšŒπš˜πš•πš•πšŽπšŒπšπš’πš˜πš—(πšŸπšŠπš›-πšπšŸπšŠπš›)
π™»π™Ύπš†πš’πš—πš
πš„π™Ώπš’πš—πš
Restrictions
πš›πšŽπššπšžπš’πš›πšŽπš(πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚,πšŸπšŠπš›)
π™»π™Ύπš†β‰€πš„π™Ώ
Purpose

Enforce all the variables of the collection πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚ to take a value within the interval [π™»π™Ύπš†,πš„π™Ώ].

Example
(2,8,2,1,9)

The πšπš˜πš–πšŠπš’πš— constraint holds since all the values 2, 8 and 2 of its first argument are greater than or equal to its second argument π™»π™Ύπš†=1 and less than or equal to its third argument πš„π™Ώ=9.

Typical
|πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚|>1
π™»π™Ύπš†<πš„π™Ώ
Symmetries
  • Items of πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚ are permutable.

  • An occurrence of a value of πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚.πšŸπšŠπš› can be replaced by any other value in [π™»π™Ύπš†,πš„π™Ώ].

  • π™»π™Ύπš† can be decreased.

  • πš„π™Ώ can be increased.

  • One and the same constant can be added to the πšŸπšŠπš› attribute of all items of πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚ as well as to π™»π™Ύπš† and πš„π™Ώ.

Remark

The πšπš˜πš–πšŠπš’πš— constraint is called πšπš˜πš– in Gecode (http://www.gecode.org/).

Reformulation

The πšπš˜πš–πšŠπš’πš—(βŒ©πšŸπšŠπš›-V 1 ,πšŸπšŠπš›-V 2 ,...,πšŸπšŠπš›-V |πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚| βŒͺ,π™»π™Ύπš†,πš„π™Ώ) constraint can be expressed in term of the conjunction

Β Β Β V 1 β‰₯π™»π™Ύπš† ∧ V 1 β‰€πš„π™Ώ,

Β Β Β V 2 β‰₯π™»π™Ύπš† ∧ V 2 β‰€πš„π™Ώ,

Β Β Β Β ..................

Β Β Β V |πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚| β‰₯π™»π™Ύπš† ∧ V |πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚| β‰€πš„π™Ώ.

Systems

member in Choco, dom in Gecode, domain in SICStus.

See also

common keyword: πš’πš—, πš’πš—_πš’πš—πšπšŽπš›πšŸπšŠπš•Β (domain definition).

uses in its reformulation: πšπš›πšŽπšŽ_πš›πšŠπš—πšπšŽ.

Keywords

constraint type: predefined constraint, value constraint.

modelling: interval, domain definition.