Global Constraint Catalog: Cmax

5.242. max_index

DESCRIPTION

LINKS

GRAPH

Origin

N. Beldiceanu

Constraint

$𝚖𝚊𝚡_𝚒𝚗𝚍𝚎𝚡 (𝙼𝙰𝚇_𝙸𝙽𝙳𝙴𝚇, 𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂)$

Arguments

$𝙼𝙰𝚇_𝙸𝙽𝙳𝙴𝚇$	$𝚍𝚟𝚊𝚛$
$𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂$	$𝚌𝚘𝚕𝚕𝚎𝚌𝚝𝚒𝚘𝚗 (𝚒𝚗𝚍𝚎𝚡 - 𝚒𝚗𝚝, 𝚟𝚊𝚛 - 𝚍𝚟𝚊𝚛)$

Restrictions

| 𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 | > 0

𝙼𝙰𝚇_𝙸𝙽𝙳𝙴𝚇 \geq 0

𝙼𝙰𝚇_𝙸𝙽𝙳𝙴𝚇 \leq | 𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 |

𝚛𝚎𝚚𝚞𝚒𝚛𝚎𝚍

(𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂, [𝚒𝚗𝚍𝚎𝚡, 𝚟𝚊𝚛])

𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 . 𝚒𝚗𝚍𝚎𝚡 \geq 1

𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 . 𝚒𝚗𝚍𝚎𝚡 \leq | 𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 |

𝚍𝚒𝚜𝚝𝚒𝚗𝚌𝚝

(𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂, 𝚒𝚗𝚍𝚎𝚡)

Purpose

$𝙼𝙰𝚇_𝙸𝙽𝙳𝙴𝚇$ is one of the indices of the collection of variables $𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂$ corresponding to its maximum value.

Example

(\begin{matrix} 3, 〈\begin{matrix} 𝚒𝚗𝚍𝚎𝚡 - 1 & 𝚟𝚊𝚛 - 3, \\ 𝚒𝚗𝚍𝚎𝚡 - 2 & 𝚟𝚊𝚛 - 2, \\ 𝚒𝚗𝚍𝚎𝚡 - 3 & 𝚟𝚊𝚛 - 7, \\ 𝚒𝚗𝚍𝚎𝚡 - 4 & 𝚟𝚊𝚛 - 2, \\ 𝚒𝚗𝚍𝚎𝚡 - 5 & 𝚟𝚊𝚛 - 7 \end{matrix}〉 \end{matrix})

The attribute $𝚟𝚊𝚛 = 7$ of the third and fifth items of the collection $𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂$ is the maximum value over values $3, 2, 7, 2, 7$ . Consequently, the $𝚖𝚊𝚡_𝚒𝚗𝚍𝚎𝚡$ constraint holds since its first argument $𝙼𝙰𝚇_𝙸𝙽𝙳𝙴𝚇$ is set to $3 \in {3, 5}$ .

Typical

| 𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 | > 0

𝚛𝚊𝚗𝚐𝚎

(𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 . 𝚟𝚊𝚛) > 1

Symmetries

Items of $𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂$ are permutable.
One and the same constant can be added to the $𝚟𝚊𝚛$ attribute of all items of $𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂$ .

See also

comparison swapped: $𝚖𝚒𝚗_𝚒𝚗𝚍𝚎𝚡$ .

Keywords

characteristic of a constraint: maximum.

constraint type: order constraint.

modelling: functional dependency.

Arc input(s)

$𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂$

Arc generator

𝐶𝐿𝐼𝑄𝑈𝐸

\mapsto 𝚌𝚘𝚕𝚕𝚎𝚌𝚝𝚒𝚘𝚗 (𝚟𝚊𝚛𝚒𝚊𝚋𝚕𝚎𝚜 1, 𝚟𝚊𝚛𝚒𝚊𝚋𝚕𝚎𝚜 2)

Arc arity

Arc constraint(s)

⋁ (\begin{matrix} 𝚟𝚊𝚛𝚒𝚊𝚋𝚕𝚎𝚜 1 . 𝚔𝚎𝚢 = 𝚟𝚊𝚛𝚒𝚊𝚋𝚕𝚎𝚜 2 . 𝚔𝚎𝚢, \\ 𝚟𝚊𝚛𝚒𝚊𝚋𝚕𝚎𝚜 1 . 𝚟𝚊𝚛 > 𝚟𝚊𝚛𝚒𝚊𝚋𝚕𝚎𝚜 2 . 𝚟𝚊𝚛 \end{matrix})

Graph property(ies)

𝐎𝐑𝐃𝐄𝐑

(0, 0, 𝚒𝚗𝚍𝚎𝚡) = 𝙼𝙰𝚇_𝙸𝙽𝙳𝙴𝚇

Graph model

Parts (A) and (B) of Figure 5.242.1 respectively show the initial and final graph associated with the Example slot. Since we use the $𝐎𝐑𝐃𝐄𝐑$ graph property, the vertex of rank 0 (without considering the loops) of the final graph is outlined with a thick circle.

Figure 5.242.1. Initial and final graph of the $𝚖𝚊𝚡_𝚒𝚗𝚍𝚎𝚡$ constraint


(a)	(b)

Global Constraint Catalog

5. Global Constraint Catalogue

5.242. max_index

Figure 5.242.1. Initial and final graph of the 𝚖𝚊𝚡_𝚒𝚗𝚍𝚎𝚡 constraint

Figure 5.242.1. Initial and final graph of the $𝚖𝚊𝚡_𝚒𝚗𝚍𝚎𝚡$ constraint