Global Constraint Catalog: Cincomparable

5.184. incomparable

DESCRIPTION

LINKS

Origin

Inspired by incomparable rectangles.

Constraint

$𝚒𝚗𝚌𝚘𝚖𝚙𝚊𝚛𝚊𝚋𝚕𝚎 (𝚅𝙴𝙲𝚃𝙾𝚁 1, 𝚅𝙴𝙲𝚃𝙾𝚁 2)$

Synonym

$𝚒𝚗𝚌𝚘𝚖𝚙𝚊𝚛𝚊𝚋𝚕𝚎𝚜$ .

Arguments

$𝚅𝙴𝙲𝚃𝙾𝚁 1$	$𝚌𝚘𝚕𝚕𝚎𝚌𝚝𝚒𝚘𝚗 (𝚟𝚊𝚛 - 𝚍𝚟𝚊𝚛)$
$𝚅𝙴𝙲𝚃𝙾𝚁 2$	$𝚌𝚘𝚕𝚕𝚎𝚌𝚝𝚒𝚘𝚗 (𝚟𝚊𝚛 - 𝚍𝚟𝚊𝚛)$

Restrictions

𝚛𝚎𝚚𝚞𝚒𝚛𝚎𝚍

(𝚅𝙴𝙲𝚃𝙾𝚁 1, 𝚟𝚊𝚛)

𝚛𝚎𝚚𝚞𝚒𝚛𝚎𝚍

(𝚅𝙴𝙲𝚃𝙾𝚁 2, 𝚟𝚊𝚛)

| 𝚅𝙴𝙲𝚃𝙾𝚁 1 | \geq 1

| 𝚅𝙴𝙲𝚃𝙾𝚁 2 | \geq 1

| 𝚅𝙴𝙲𝚃𝙾𝚁 1 | = | 𝚅𝙴𝙲𝚃𝙾𝚁 2 |

Purpose

Enforce that when the components of $𝚅𝙴𝙲𝚃𝙾𝚁 1$ and $𝚅𝙴𝙲𝚃𝙾𝚁 2$ are ordered, and respectively denoted by $𝚂𝚅𝙴𝙲𝚃𝙾𝚁 1$ and $𝚂𝚅𝙴𝙲𝚃𝙾𝚁 2$ , we neither have $𝚂𝚅𝙴𝙲𝚃𝙾𝚁 1 [i] . 𝚟𝚊𝚛 \leq 𝚂𝚅𝙴𝙲𝚃𝙾𝚁 2 [i] . 𝚟𝚊𝚛$ (for all $i \in [1, | 𝚂𝚅𝙴𝙲𝚃𝙾𝚁 1 |]$ ) nor have $𝚂𝚅𝙴𝙲𝚃𝙾𝚁 2 [i] . 𝚟𝚊𝚛 \leq 𝚂𝚅𝙴𝙲𝚃𝙾𝚁 1 [i] . 𝚟𝚊𝚛$ (for all $i \in [1, | 𝚂𝚅𝙴𝙲𝚃𝙾𝚁 1 |]$ ).

Example