5.326. sum_ctr

DESCRIPTIONLINKSGRAPH
Origin

Arithmetic constraint.

Constraint

πšœπšžπš–_πšŒπšπš›(πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚,π™²πšƒπš,πš…π™°πš)

Synonyms

πšŒπš˜πš—πšœπšπšŠπš—πš_πšœπšžπš–, πšœπšžπš–, πš•πš’πš—πšŽπšŠπš›, πšœπšŒπšŠπš•πšŠπš›_πš™πš›πš˜πšπšžπšŒπ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™²πšƒπšπšŠπšπš˜πš–
πš…π™°πšπšπšŸπšŠπ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™²πšƒπšβˆˆ[=,β‰ ,<,β‰₯,>,≀]
Purpose

Constraint the sum of a set of domain variables. More precisely, let πš‚ denote the sum of the variables of the πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚ collection (when the collection is empty the corresponding sum is equal to 0). Enforce the following constraint to hold: πš‚ π™²πšƒπš πš…π™°πš.

Example
(1,1,4,=,6)

The πšœπšžπš–_πšŒπšπš› constraint holds since the condition 1+1+4=6 is satisfied.

Symmetry

Items of πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚ are permutable.

Remark

When π™²πšƒπš corresponds to = this constraint is referenced under the names πšŒπš˜πš—πšœπšπšŠπš—πš_πšœπšžπš– in KOALOG (http://www.koalog.com/php/index.php) and πšœπšžπš– in JaCoP (http://www.jacop.eu/).

Systems

equation in Choco, linear in Gecode, scalar_product in SICStus.

Used in

πš‹πš’πš—_πš™πšŠπšŒπš”πš’πš—πš, πšŒπšžπš–πšžπš•πšŠπšπš’πšŸπšŽ, πšŒπšžπš–πšžπš•πšŠπšπš’πšŸπšŽ_πšŒπš˜πš—πšŸπšŽπš‘, πšŒπšžπš–πšžπš•πšŠπšπš’πšŸπšŽ_πš πš’πšπš‘_πš•πšŽπšŸπšŽπš•_𝚘𝚏_πš™πš›πš’πš˜πš›πš’πšπš’, πšŒπšžπš–πšžπš•πšŠπšπš’πšŸπšŽπšœ, πš’πš—πšπšŽπš‘πšŽπš_πšœπšžπš–, πš’πš—πšπšŽπš›πšŸπšŠπš•_πšŠπš—πš_πšœπšžπš–, πš›πšŽπš•πšŠπš‘πšŽπš_πšœπš•πš’πšπš’πš—πš_πšœπšžπš–, πšœπš•πš’πšπš’πš—πš_πšœπšžπš–, πšœπš•πš’πšπš’πš—πš_πšπš’πš–πšŽ_πš πš’πš—πšπš˜πš _πšœπšžπš–.

See also

assignment dimension added: πš’πš—πšπšŽπš›πšŸπšŠπš•_πšŠπš—πš_πšœπšžπš–Β (assignment dimension corresponding to intervals is added).

common keyword: πšŠπš›πš’πšπš‘_πšœπš•πš’πšπš’πš—πš, πš™πš›πš˜πšπšžπšŒπš_πšŒπšπš›, πš›πšŠπš—πšπšŽ_πšŒπšπš›Β (arithmetic constraint), πšœπšžπš–Β (sum), πšœπšžπš–_𝚜𝚎𝚝 (arithmetic constraint).

generalisation: πšœπšŒπšŠπš•πšŠπš›_πš™πš›πš˜πšπšžπšŒπšΒ (arithmetic constraint where all coefficients are not necessarly equal to 1).

system of constraints: πšœπš•πš’πšπš’πš—πš_πšœπšžπš–.

Keywords

characteristic of a constraint: sum.

constraint type: arithmetic constraint.

Arc input(s)

πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚

Arc generator
π‘†πΈπΏπΉβ†¦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)

Arc arity
Arc constraint(s)
πšƒπšπš„π™΄
Graph property(ies)
π’π”πŒ(πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚,πšŸπšŠπš›) π™²πšƒπš πš…π™°πš

Graph model

Since we want to keep all the vertices of the initial graph we use the 𝑆𝐸𝐿𝐹 arc generator together with the πšƒπšπš„π™΄ arc constraint. This predefined arc constraint always holds.

PartsΒ (A) andΒ (B) of FigureΒ 5.326.1 respectively show the initial and final graph associated with the Example slot. Since we use the πšƒπšπš„π™΄ arc constraint both graphs are identical.

Figure 5.326.1. Initial and final graph of the πšœπšžπš–_πšŒπšπš› constraint
ctrs/sum_ctrActrs/sum_ctrB
(a) (b)