Global Constraint Catalog: Cmaximum

5.211. maximum_modulo

DESCRIPTION

LINKS

GRAPH

Origin

Derived from $𝚖𝚊𝚡𝚒𝚖𝚞𝚖$ .

Constraint

$𝚖𝚊𝚡𝚒𝚖𝚞𝚖_𝚖𝚘𝚍𝚞𝚕𝚘 (𝙼𝙰𝚇, 𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂, 𝙼)$

Arguments

$𝙼𝙰𝚇$	$𝚍𝚟𝚊𝚛$
$𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂$	$𝚌𝚘𝚕𝚕𝚎𝚌𝚝𝚒𝚘𝚗 (𝚟𝚊𝚛 - 𝚍𝚟𝚊𝚛)$
$𝙼$	$𝚒𝚗𝚝$

Restrictions

| 𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 | > 0

𝙼 > 0

𝚛𝚎𝚚𝚞𝚒𝚛𝚎𝚍

(𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂, 𝚟𝚊𝚛)

Purpose

$𝙼𝙰𝚇$ is a maximum value of the collection of domain variables $𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂$ according to the following partial ordering: $(X \mod 𝙼) < (Y \mod 𝙼)$ .

Example

(5, 〈9, 1, 7, 6, 5〉, 3)

The $𝚖𝚊𝚡𝚒𝚖𝚞𝚖_𝚖𝚘𝚍𝚞𝚕𝚘$ constraint holds since its first argument $𝙼𝙰𝚇$ is set to value 5, where $5 \mod 3 = 2$ is greater than or equal to all the expressions $9 \mod 3 = 0$ , $1 \mod 3 = 1$ , $7 \mod 3 = 1$ and $6 \mod 3 = 0$ .

Symmetry

Items of $𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂$ are permutable.

specialisation: $𝚖𝚊𝚡𝚒𝚖𝚞𝚖$ ( $𝚟𝚊𝚛𝚒𝚊𝚋𝚕𝚎 \mod 𝚌𝚘𝚗𝚜𝚝𝚊𝚗𝚝$ replaced by $𝚟𝚊𝚛𝚒𝚊𝚋𝚕𝚎$ ).

Keywords

characteristic of a constraint: modulo, maximum.

constraint type: order constraint.

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 \mod 𝙼 > 𝚟𝚊𝚛𝚒𝚊𝚋𝚕𝚎𝚜 2 . 𝚟𝚊𝚛 \mod 𝙼 \end{matrix})

Graph property(ies)

𝐎𝐑𝐃𝐄𝐑

(0, 𝙼𝙸𝙽𝙸𝙽𝚃, 𝚟𝚊𝚛) = 𝙼𝙰𝚇

Graph model

Parts (A) and (B) of Figure 5.211.1 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 5.211.1. Initial and final graph of the $𝚖𝚊𝚡𝚒𝚖𝚞𝚖_𝚖𝚘𝚍𝚞𝚕𝚘$ constraint


(a)	(b)

Global Constraint Catalog

5. Global Constraint Catalogue

5.211. maximum_modulo

Figure 5.211.1. Initial and final graph of the $𝚖𝚊𝚡𝚒𝚖𝚞𝚖_𝚖𝚘𝚍𝚞𝚕𝚘$ constraint

W3C: XHTML - last update: 2010-12-6. SD.

Global Constraint Catalog

5. Global Constraint Catalogue

5.211. maximum_modulo

Figure 5.211.1. Initial and final graph of the 𝚖𝚊𝚡𝚒𝚖𝚞𝚖_𝚖𝚘𝚍𝚞𝚕𝚘 constraint

W3C: XHTML - last update: 2010-12-6. SD.

Figure 5.211.1. Initial and final graph of the $𝚖𝚊𝚡𝚒𝚖𝚞𝚖_𝚖𝚘𝚍𝚞𝚕𝚘$ constraint