5.281. same_intersection

DESCRIPTIONLINKSGRAPH
Origin

Derived from πšœπšŠπš–πšŽ and πšŒπš˜πš–πš–πš˜πš—.

Constraint

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—(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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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

Each value, which occurs both in the πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚1 and in the πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚2 collections, has the same number of occurrences in πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚1 as well as in πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚2.

Example
πšŸπšŠπš›-1,πšŸπšŠπš›-9,πšŸπšŠπš›-1,πšŸπšŠπš›-5,πšŸπšŠπš›-2,πšŸπšŠπš›-1,πšŸπšŠπš›-9,πšŸπšŠπš›-1,πšŸπšŠπš›-1,πšŸπšŠπš›-1,πšŸπšŠπš›-3,πšŸπšŠπš›-5,πšŸπšŠπš›-8

First note that the values, which occur both in πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚1=〈1,9,1,5,2,1βŒͺ as well as in πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚2=〈9,1,1,1,3,5,8βŒͺ correspond to values 1, 5, and 9. Consequently, the 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— constraint holds since these values 1, 5, and 9 have the same number of occurrences in both collections (i.e.,Β they respectively occur 3, 1, and 1 times within 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).

Symmetries
  • Arguments are permutable w.r.t. permutation (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šŒπš˜πš–πš–πš˜πš—, 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—Β (constraint on the intersection).

implied by: 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šŠπš–πšŽ.

Keywords

constraint arguments: constraint between two collections of variables.

constraint type: constraint on the intersection.

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)
for all connected components: ππ’πŽπ”π‘π‚π„=ππ’πˆππŠ

Graph model

PartsΒ (A) andΒ (B) of FigureΒ 5.281.1 respectively show the initial and final graph associated with the Example slot. The 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— constraint holds since each connected component of the final graph has the same number of sources and sinks. Note that all the vertices corresponding to the variables that take values 2, 3 or 8 were removed from the final graph since there is no arc for which the associated equality constraint holds.

Figure 5.281.1. Initial and final graph of the 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— constraint
ctrs/same_intersectionActrs/same_intersectionB
(a) (b)