5.237. nset_of_consecutive_values

DESCRIPTIONLINKSGRAPH
Origin

N.Β Beldiceanu

Constraint

πš—πšœπšŽπš_𝚘𝚏_πšŒπš˜πš—πšœπšŽπšŒπšžπšπš’πšŸπšŽ_πšŸπšŠπš•πšžπšŽπšœ(𝙽,πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚)

Arguments
π™½πšπšŸπšŠπš›
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›)
Restrictions
𝙽β‰₯1
𝙽≀|πš…π™°πšπ™Έπ™°π™±π™»π™΄π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‚,πšŸπšŠπš›)
Purpose

𝙽 is the number of set of consecutive values used by the variables of the collection πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚.

Example
2,πšŸπšŠπš›-3,πšŸπšŠπš›-1,πšŸπšŠπš›-7,πšŸπšŠπš›-1,πšŸπšŠπš›-1,πšŸπšŠπš›-2,πšŸπšŠπš›-8

In the example, the two parts 3,1,1,1,2 and 7,8 take respectively their values in the following sets of consecutive values {1,2,3} and {7,8}. Consequently, the πš—πšœπšŽπš_𝚘𝚏_πšŒπš˜πš—πšœπšŽπšŒπšžπšπš’πšŸπšŽ_πšŸπšŠπš•πšžπšŽπšœ constraint holds since its first argument 𝙽=2 is set to the number of sets of consecutive values.

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

  • All occurrences of two distinct values of πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚.πšŸπšŠπš› can be swapped.

  • One and the same constant can be added to the πšŸπšŠπš› attribute of all items of πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚.

Usage

Used for specifying the fact that the values have to be used in a compact way is achieved by setting 𝙽 to 1.

See also

common keyword: πš–πšŠπš‘_πšœπš’πš£πšŽ_𝚜𝚎𝚝_𝚘𝚏_πšŒπš˜πš—πšœπšŽπšŒπšžπšπš’πšŸπšŽ_πšŸπšŠπš›, πš–πš’πš—_πšœπš’πš£πšŽ_𝚜𝚎𝚝_𝚘𝚏_πšŒπš˜πš—πšœπšŽπšŒπšžπšπš’πšŸπšŽ_πšŸπšŠπš›Β (consecutive values).

Keywords

characteristic of a constraint: consecutive values.

constraint type: value constraint.

final graph structure: strongly connected component.

Arc input(s)

πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚

Arc generator
πΆπΏπΌπ‘„π‘ˆπΈβ†¦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šŠπš‹πšœ(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›)≀1
Graph property(ies)
𝐍𝐒𝐂𝐂=𝙽

Graph model

Since the arc constraint is symmetric each strongly connected component of the final graph corresponds exactly to one connected component of the final graph.

PartsΒ (A) andΒ (B) of FigureΒ 5.237.1 respectively show the initial and final graph associated with the Example slot. Since we use the 𝐍𝐒𝐂𝐂 graph property, we show the two strongly connected components of the final graph.

Figure 5.237.1. Initial and final graph of the πš—πšœπšŽπš_𝚘𝚏_πšŒπš˜πš—πšœπšŽπšŒπšžπšπš’πšŸπšŽ_πšŸπšŠπš•πšžπšŽπšœ constraint
ctrs/nset_of_consecutive_valuesActrs/nset_of_consecutive_valuesB
(a) (b)