5.351. vec_eq_tuple

DESCRIPTIONLINKSGRAPH
Origin

Used for defining πš’πš—_πš›πšŽπš•πšŠπšπš’πš˜πš—.

Constraint

𝚟𝚎𝚌_𝚎𝚚_πšπšžπš™πš•πšŽ(πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚,πšƒπš„π™Ώπ™»π™΄)

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šƒπš„π™Ώπ™»π™΄πšŒπš˜πš•πš•πšŽπšŒπšπš’πš˜πš—(πšŸπšŠπš•-π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š›πšŽπššπšžπš’πš›πšŽπš(πšƒπš„π™Ώπ™»π™΄,πšŸπšŠπš•)
|πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚|=|πšƒπš„π™Ώπ™»π™΄|
Purpose

Enforce a vector of domain variables to be equal to a tuple of values.

Example
5,3,3,5,3,3

The 𝚟𝚎𝚌_𝚎𝚚_πšπšžπš™πš•πšŽ constraint holds since the first, the second and the third items of πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚=〈5,3,3βŒͺ are respectively equal to the first, the second and the third items of πšƒπš„π™Ώπ™»π™΄=〈5,3,3βŒͺ.

Symmetries
  • Arguments are permutable w.r.t. permutation (πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚,πšƒπš„π™Ώπ™»π™΄).

  • Items of πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚ and πšƒπš„π™Ώπ™»π™΄ are permutable (same permutation used).

Used in

πš’πš—_πš›πšŽπš•πšŠπšπš’πš˜πš—.

See also

generalisation: πš•πšŽπš‘_πšŽπššπšžπšŠπš•Β (πš’πš—πšπšŽπšπšŽπš› replaced by πšŸπšŠπš›πš’πšŠπš‹πš•πšŽ in second argument).

implies: πš•πšŽπš‘_πšŽπššπšžπšŠπš•.

Keywords

characteristic of a constraint: tuple.

constraint type: value constraint.

filtering: arc-consistency.

Arc input(s)

πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚ πšƒπš„π™Ώπ™»π™΄

Arc generator
π‘ƒπ‘…π‘‚π·π‘ˆπΆπ‘‡(=)β†¦πšŒπš˜πš•πš•πšŽπšŒπšπš’πš˜πš—(πšŸπšŠπš›πš’πšŠπš‹πš•πšŽπšœ,πšπšžπš™πš•πšŽ)

Arc arity
Arc constraint(s)
πšŸπšŠπš›πš’πšŠπš‹πš•πšŽπšœ.πšŸπšŠπš›=πšπšžπš™πš•πšŽ.πšŸπšŠπš•
Graph property(ies)
𝐍𝐀𝐑𝐂=|πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚|

Graph model

PartsΒ (A) andΒ (B) of FigureΒ 5.351.1 respectively show the initial and final graph associated with the Example slot. Since we use the 𝐍𝐀𝐑𝐂 graph property, the arcs of the final graph are stressed in bold.

Figure 5.351.1. Initial and final graph of the 𝚟𝚎𝚌_𝚎𝚚_πšπšžπš™πš•πšŽ constraint
ctrs/vec_eq_tupleActrs/vec_eq_tupleB
(a) (b)
Signature

Since we use the arc generator π‘ƒπ‘…π‘‚π·π‘ˆπΆπ‘‡(=) on the collections πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚ and πšƒπš„π™Ώπ™»π™΄, and because of the restriction |πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚|=|πšƒπš„π™Ώπ™»π™΄|, the maximum number of arcs of the final graph is equal to |πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚|. Therefore we can rewrite the graph property 𝐍𝐀𝐑𝐂=|πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚| to 𝐍𝐀𝐑𝐂β‰₯|πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚| and simplify 𝐍𝐀𝐑𝐂 Β― Μ² to 𝐍𝐀𝐑𝐂 Β―.