5.218. leq_cst

DESCRIPTIONLINKS
Origin

Arithmetic.

Constraint

𝚕𝚎𝚚_𝚌𝚜𝚝(𝚅𝙰𝚁1,𝚅𝙰𝚁2,𝙲𝚂𝚃2)

Arguments
𝚅𝙰𝚁1𝚍𝚟𝚊𝚛
𝚅𝙰𝚁2𝚍𝚟𝚊𝚛
𝙲𝚂𝚃2𝚒𝚗𝚝
Purpose

Enforce the fact that the first variable is less than or equal to the sum of the second variable and the constant.

Example
(5,2,4)

The 𝚕𝚎𝚚_𝚌𝚜𝚝 constraint holds since 5 is less than or equal to 2+4.

Typical
𝙲𝚂𝚃2≠0
𝚅𝙰𝚁1<𝚅𝙰𝚁2+𝙲𝚂𝚃2
Symmetries

  • Arguments are permutable w.r.t. permutation (𝚅𝙰𝚁1) (𝚅𝙰𝚁2,𝙲𝚂𝚃2).

  • 𝚅𝙰𝚁1 can be replaced by any value ≤𝚅𝙰𝚁2+𝙲𝚂𝚃2.

  • 𝚅𝙰𝚁2 can be replaced by any value ≥𝚅𝙰𝚁1-𝙲𝚂𝚃2.

  • 𝙲𝚂𝚃2 can be replaced by any value ≥𝚅𝙰𝚁1-𝚅𝙰𝚁2.

See also

common keyword: 𝚐𝚎𝚚_𝚌𝚜𝚝 (binary constraint,arithmetic constraint).

implied by: 𝚍𝚒𝚜𝚝𝚊𝚗𝚌𝚎, 𝚎𝚚_𝚌𝚜𝚝.

specialisation: 𝚕𝚎𝚚 (𝚌𝚘𝚗𝚜𝚝𝚊𝚗𝚝 set to 0).

Keywords

constraint arguments: binary constraint.

constraint type: predefined constraint, arithmetic constraint.

filtering: arc-consistency.

modelling exercises: metro.