5.290. size_max_seq_alldifferent

DESCRIPTIONLINKSGRAPH
Origin

N.Β Beldiceanu

Constraint

πšœπš’πš£πšŽ_πš–πšŠπš‘_𝚜𝚎𝚚_πšŠπš•πš•πšπš’πšπšπšŽπš›πšŽπš—πš(πš‚π™Έπš‰π™΄,πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚)

Synonyms

πšœπš’πš£πšŽ_πš–πšŠπš‘πš’πš–πšŠπš•_πšœπšŽπššπšžπšŽπš—πšŒπšŽ_πšŠπš•πš•πšπš’πšπš, πšœπš’πš£πšŽ_πš–πšŠπš‘πš’πš–πšŠπš•_πšœπšŽπššπšžπšŽπš—πšŒπšŽ_πšŠπš•πš•πšπš’πšœπšπš’πš—πšŒπš, πšœπš’πš£πšŽ_πš–πšŠπš‘πš’πš–πšŠπš•_πšœπšŽπššπšžπšŽπš—πšŒπšŽ_πšŠπš•πš•πšπš’πšπšπšŽπš›πšŽπš—πš.

Arguments
πš‚π™Έπš‰π™΄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šŸπšŠπš›-πšπšŸπšŠπš›)
Restrictions
πš‚π™Έπš‰π™΄β‰₯0
πš‚π™Έπš‰π™΄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šŸπšŠπš›)
Purpose

πš‚π™Έπš‰π™΄ is the size of the maximal sequence (among all possible sequences of consecutive variables of the collection πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚) for which the πšŠπš•πš•πšπš’πšπšπšŽπš›πšŽπš—πš constraint holds.

Example
4,πšŸπšŠπš›-2,πšŸπšŠπš›-2,πšŸπšŠπš›-4,πšŸπšŠπš›-5,πšŸπšŠπš›-2,πšŸπšŠπš›-7,πšŸπšŠπš›-4

The πšœπš’πš£πšŽ_πš–πšŠπš‘_𝚜𝚎𝚚_πšŠπš•πš•πšπš’πšπšπšŽπš›πšŽπš—πš constraint holds since the constraint πšŠπš•πš•πšπš’πšπšπšŽπš›πšŽπš—πš(βŒ©πšŸπšŠπš›-4,πšŸπšŠπš›-5,πšŸπšŠπš›-2,πšŸπšŠπš›-7βŒͺ) holds and since the following three constraints do not hold:

Symmetry

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

common keyword: 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šŽπš—_πšŠπš•πš•πšπš’πšπšπšŽπš›πšŽπš—πš, πšœπš’πš£πšŽ_πš–πšŠπš‘_πšœπšπšŠπš›πšπš’πš—πš_𝚜𝚎𝚚_πšŠπš•πš•πšπš’πšπšπšŽπš›πšŽπš—πšΒ (all different,disequality).

Keywords

characteristic of a constraint: all different, disequality, hypergraph.

combinatorial object: sequence.

constraint type: sliding sequence constraint, conditional constraint.

Arc input(s)

πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚

Arc generator
𝑃𝐴𝑇𝐻_π‘β†¦πšŒπš˜πš•πš•πšŽπšŒπšπš’πš˜πš—

Arc arity
*
Arc constraint(s)
πšŠπš•πš•πšπš’πšπšπšŽπš›πšŽπš—πš(πšŒπš˜πš•πš•πšŽπšŒπšπš’πš˜πš—)
Graph property(ies)
𝐍𝐀𝐑𝐂=πš‚π™Έπš‰π™΄

Graph model

Note that this is an example of global constraint where the arc constraints do not have the same arity. However they correspond to the same type of constraint.