5.239. nvalue_on_intersection

DESCRIPTIONLINKSGRAPH
Origin

Derived from πšŒπš˜πš–πš–πš˜πš— and πš—πšŸπšŠπš•πšžπšŽ.

Constraint

πš—πšŸπšŠπš•πšžπšŽ_πš˜πš—_πš’πš—πšπšŽπš›πšœπšŽπšŒπšπš’πš˜πš—(π™½πš…π™°π™»,πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚1,πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚2)

Arguments
π™½πš…π™°π™»πšπšŸπšŠπš›
πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚1π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š…π™°πšπ™Έπ™°π™±π™»π™΄πš‚2π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›)
Restrictions
π™½πš…π™°π™»β‰₯0
π™½πš…π™°π™»β‰€|πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚1|
π™½πš…π™°π™»β‰€|πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚2|
πš›πšŽπššπšžπš’πš›πšŽπš(πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚1,πšŸπšŠπš›)
πš›πšŽπššπšžπš’πš›πšŽπš(πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚2,πšŸπšŠπš›)
Purpose

π™½πš…π™°π™» is the number of distinct values that both occur in the πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚1 and πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚2 collections.

Example
2,1,9,1,5,πšŸπšŠπš›-2,πšŸπšŠπš›-1,πšŸπšŠπš›-9,πšŸπšŠπš›-9,πšŸπšŠπš›-6,πšŸπšŠπš›-9

Note that the two collections 〈1,9,1,5βŒͺ and 〈2,1,9,9,6,9βŒͺ share two values in common (i.e.,Β values 1 and 9). Consequently the πš—πšŸπšŠπš•πšžπšŽ_πš˜πš—_πš’πš—πšπšŽπš›πšœπšŽπšŒπšπš’πš˜πš— constraint holds since its first argument π™½πš…π™°π™» is set to 2.

Symmetries
  • Arguments are permutable w.r.t. permutation (π™½πš…π™°π™») (πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚1,πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚2).

  • Items of πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚1 are permutable.

  • Items of πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚2 are permutable.

  • All occurrences of two distinct values in πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚1.πšŸπšŠπš› or πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚2.πšŸπšŠπš› can be swapped; all occurrences of a value in πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚1.πšŸπšŠπš› or πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚2.πšŸπšŠπš› can be renamed to any unused value.

See also

common keyword: πšŠπš•πš•πšπš’πšπšπšŽπš›πšŽπš—πš_πš˜πš—_πš’πš—πšπšŽπš›πšœπšŽπšŒπšπš’πš˜πš—, πšŒπš˜πš–πš–πš˜πš—, πšœπšŠπš–πšŽ_πš’πš—πšπšŽπš›πšœπšŽπšŒπšπš’πš˜πš—Β (constraint on the intersection).

root concept: πš—πšŸπšŠπš•πšžπšŽ.

Keywords

constraint type: counting constraint, constraint on the intersection.

final graph structure: connected component.

modelling: number of distinct values.

Arc input(s)

πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚1 πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚2

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šœ1,πšŸπšŠπš›πš’πšŠπš‹πš•πšŽπšœ2)

Arc arity
Arc constraint(s)
πšŸπšŠπš›πš’πšŠπš‹πš•πšŽπšœ1.πšŸπšŠπš›=πšŸπšŠπš›πš’πšŠπš‹πš•πšŽπšœ2.πšŸπšŠπš›
Graph property(ies)
𝐍𝐂𝐂=π™½πš…π™°π™»

Graph model

PartsΒ (A) andΒ (B) of FigureΒ 5.239.1 respectively show the initial and final graph associated with the Example slot. Since we use the 𝐍𝐂𝐂 graph property we show the connected components of the final graph. The variable π™½πš…π™°π™» is equal to this number of connected components. Note that all the vertices corresponding to the variables that take values 5, 2 or 6 were removed from the final graph since there is no arc for which the associated equality constraint holds.

Figure 5.239.1. Initial and final graph of the πš—πšŸπšŠπš•πšžπšŽ_πš˜πš—_πš’πš—πšπšŽπš›πšœπšŽπšŒπšπš’πš˜πš— constraint
ctrs/nvalue_on_intersectionActrs/nvalue_on_intersectionB
(a) (b)