5.206. max_index

DESCRIPTIONLINKSGRAPH
Origin

N.Β Beldiceanu

Constraint

πš–πšŠπš‘_πš’πš—πšπšŽπš‘(π™Όπ™°πš‡_π™Έπ™½π™³π™΄πš‡,πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚)

Arguments
π™Όπ™°πš‡_π™Έπ™½π™³π™΄πš‡π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š’πš—πšπšŽπš‘-πš’πš—πš,πšŸπšŠπš›-πšπšŸπšŠπš›)
Restrictions
|πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚|>0
π™Όπ™°πš‡_π™Έπ™½π™³π™΄πš‡β‰₯0
π™Όπ™°πš‡_π™Έπ™½π™³π™΄πš‡β‰€|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š’πš—πšπšŽπš‘,πšŸπšŠπš›])
πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚.πš’πš—πšπšŽπš‘β‰₯1
πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚.πš’πš—πšπšŽπš‘β‰€|πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚|
πšπš’πšœπšπš’πš—πšŒπš(πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚,πš’πš—πšπšŽπš‘)
Purpose

π™Όπ™°πš‡_π™Έπ™½π™³π™΄πš‡ is the index of the variables corresponding to the maximum value of the collection of variables πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚.

Example
3,πš’πš—πšπšŽπš‘-1πšŸπšŠπš›-3,πš’πš—πšπšŽπš‘-2πšŸπšŠπš›-2,πš’πš—πšπšŽπš‘-3πšŸπšŠπš›-7,πš’πš—πšπšŽπš‘-4πšŸπšŠπš›-2,πš’πš—πšπšŽπš‘-5πšŸπšŠπš›-6

The attribute πšŸπšŠπš›=7 of the third item of the collection πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚ is the maximum value over values 3,2,7,2,6. Consequently, the πš–πšŠπš‘_πš’πš—πšπšŽπš‘ constraint holds since its first argument π™Όπ™°πš‡_π™Έπ™½π™³π™΄πš‡ is set to 3.

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

  • 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‚.

See also

comparison swapped: πš–πš’πš—_πš’πš—πšπšŽπš‘.

Keywords

characteristic of a constraint: maximum.

constraint type: order constraint.

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)
β‹πšŸπšŠπš›πš’πšŠπš‹πš•πšŽπšœ1.πš”πšŽπš’=πšŸπšŠπš›πš’πšŠπš‹πš•πšŽπšœ2.πš”πšŽπš’,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)
πŽπ‘πƒπ„π‘(0,0,πš’πš—πšπšŽπš‘)=π™Όπ™°πš‡_π™Έπ™½π™³π™΄πš‡

Graph model

PartsΒ (A) andΒ (B) of FigureΒ 5.206.1 respectively show the initial and final graph associated with the Example slot. Since we use the πŽπ‘πƒπ„π‘ graph property, the vertex of rank 0 (without considering the loops) of the final graph is outlined with a thick circle.

Figure 5.206.1. Initial and final graph of the πš–πšŠπš‘_πš’πš—πšπšŽπš‘ constraint
ctrs/max_indexActrs/max_indexB
(a) (b)