5.406. twin

DESCRIPTIONLINKS
Origin

Pairs of variables related by hiden πšŽπš•πšŽπš–πšŽπš—πš constraints sharing the same table.

Constraint

πšπš πš’πš—(π™Ώπ™°π™Έπšπš‚)

Argument
π™Ώπ™°π™Έπšπš‚πšŒπš˜πš•πš•πšŽπšŒπšπš’πš˜πš—(𝚑-πšπšŸπšŠπš›,𝚒-πšπšŸπšŠπš›)
Restrictions
πš›πšŽπššπšžπš’πš›πšŽπš(π™Ώπ™°π™Έπšπš‚,𝚑)
πš›πšŽπššπšžπš’πš›πšŽπš(π™Ώπ™°π™Έπšπš‚,𝚒)
|π™Ώπ™°π™Έπšπš‚|>0
Purpose

Enforce the condition π™Ώπ™°π™Έπšπš‚[i].𝚑=uβˆ§π™Ώπ™°π™Έπšπš‚[i].𝚒=v (i∈[1,|π™Ώπ™°π™Έπšπš‚|]) β‡’ βˆ€j∈[1,|π™Ώπ™°π™Έπšπš‚|]:π™Ώπ™°π™Έπšπš‚[j].𝚑=uβ‡”π™Ώπ™°π™Έπšπš‚[j].𝚒=v.

Example
𝚑-1𝚒-8,𝚑-9𝚒-6,𝚑-1𝚒-8,𝚑-5𝚒-0,𝚑-6𝚒-7,𝚑-9𝚒-6

The πšπš πš’πš— constraint holds since 1 is paired with 8, 9 is paired with 6, 5 is paired with 0, 6 is paired with 7.

Typical
|π™Ώπ™°π™Έπšπš‚|>1
|π™Ώπ™°π™Έπšπš‚|>πš—πšŸπšŠπš•(π™Ώπ™°π™Έπšπš‚.𝚑)
|π™Ώπ™°π™Έπšπš‚|>πš—πšŸπšŠπš•(π™Ώπ™°π™Έπšπš‚.𝚒)
πš—πšŸπšŠπš•(π™Ώπ™°π™Έπšπš‚.𝚑)>1
πš—πšŸπšŠπš•(π™Ώπ™°π™Έπšπš‚.𝚒)>1
πš—πšŸπšŠπš•(π™Ώπ™°π™Έπšπš‚.𝚑)=πš—πšŸπšŠπš•(π™Ώπ™°π™Έπšπš‚.𝚒)
πš—πšŸπšŠπš•(π™Ώπ™°π™Έπšπš‚.𝚑)<|π™Ώπ™°π™Έπšπš‚|
πš—πšŸπšŠπš•(π™Ώπ™°π™Έπšπš‚.𝚒)<|π™Ώπ™°π™Έπšπš‚|
Arg. properties

Contractible wrt. π™Ώπ™°π™Έπšπš‚.

See also

implied by: πšŒπš’πš›πšŒπšžπš’πš, πšπšŽπš›πšŠπš—πšπšŽπš–πšŽπš—πš, πš™πš›πš˜πš™πšŽπš›_πšŒπš’πš›πšŒπšžπš’πš, πšœπš’πš–πš–πšŽπšπš›πš’πšŒ_πšŠπš•πš•πšπš’πšπšπšŽπš›πšŽπš—πš_πš•πš˜πš˜πš™.

related: πšŽπš•πšŽπš–πšŽπš—πšΒ (pairs linked by an element with the same table).

Keywords

characteristic of a constraint: pair.

constraint type: predefined constraint.