5.156. in_relation

DESCRIPTIONLINKSGRAPH
Origin

Constraint explicitly defined by tuples of values.

Constraint

πš’πš—_πš›πšŽπš•πšŠπšπš’πš˜πš—(πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚,πšƒπš„π™Ώπ™»π™΄πš‚_𝙾𝙡_πš…π™°π™»πš‚)

Synonyms

𝚌𝚊𝚜𝚎, πšŽπš‘πšπšŽπš—πšœπš’πš˜πš—, πšŽπš‘πšπšŽπš—πšœπš’πš˜πš—πšŠπš•, πšŽπš‘πšπšŽπš—πšœπš’πš˜πš—πšŠπš•_πšœπšžπš™πš™πš˜πš›πš, πšŽπš‘πšπšŽπš—πšœπš’πš˜πš—πšŠπš•_πšœπšžπš™πš™πš˜πš›πšπšŸπšŠ, πšŽπš‘πšπšŽπš—πšœπš’πš˜πš—πšŠπš•_πšœπšžπš™πš™πš˜πš›πšπš–πšπš, πšŽπš‘πšπšŽπš—πšœπš’πš˜πš—πšŠπš•_πšœπšžπš™πš™πš˜πš›πšπšœπšπš›, πšπšŽπšŠπšœπšπšžπš™πš•πšŽπšŠπšŒ, πšπšŠπš‹πš•πšŽ.

Types
πšƒπš„π™Ώπ™»π™΄_𝙾𝙡_πš…π™°πš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›)
πšƒπš„π™Ώπ™»π™΄_𝙾𝙡_πš…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š—πš)
Arguments
πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚πšƒπš„π™Ώπ™»π™΄_𝙾𝙡_πš…π™°πšπš‚
πšƒπš„π™Ώπ™»π™΄πš‚_𝙾𝙡_πš…π™°π™»πš‚πšŒπš˜πš•πš•πšŽπšŒπšπš’πš˜πš—(πšπšžπš™πš•πšŽ-πšƒπš„π™Ώπ™»π™΄_𝙾𝙡_πš…π™°π™»πš‚)
Restrictions
πš›πšŽπššπšžπš’πš›πšŽπš(πšƒπš„π™Ώπ™»π™΄_𝙾𝙡_πš…π™°πšπš‚,πšŸπšŠπš›)
|πšƒπš„π™Ώπ™»π™΄_𝙾𝙡_πš…π™°πšπš‚|=|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šƒπš„π™Ώπ™»π™΄_𝙾𝙡_πš…π™°π™»πš‚,πšŸπšŠπš•)
πš›πšŽπššπšžπš’πš›πšŽπš(πšƒπš„π™Ώπ™»π™΄πš‚_𝙾𝙡_πš…π™°π™»πš‚,πšπšžπš™πš•πšŽ)
Purpose

Enforce the tuple of variables πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚ to take its value out of a set of tuples of values πšƒπš„π™Ώπ™»π™΄πš‚_𝙾𝙡_πš…π™°π™»πš‚. The value of a tuple of variables 〈V 1 ,V 2 ,...,V n βŒͺ is a tuple of values 〈U 1 ,U 2 ,...,U n βŒͺ if and only if V 1 =U 1 ∧V 2 =U 2 βˆ§β‹―βˆ§V n =U n .

Example
5,3,3,πšπšžπš™πš•πšŽ-5,2,3,πšπšžπš™πš•πšŽ-5,2,6,πšπšžπš™πš•πšŽ-5,3,3

The πš’πš—_πš›πšŽπš•πšŠπšπš’πš˜πš— constraint holds since its first argument 〈5,3,3βŒͺ corresponds to the third item of the collection of tuples πšƒπš„π™Ώπ™»π™΄πš‚_𝙾𝙡_πš…π™°π™»πš‚.

Typical
|πšƒπš„π™Ώπ™»π™΄_𝙾𝙡_πš…π™°πšπš‚|>1
Symmetries
  • Items of πšƒπš„π™Ώπ™»π™΄πš‚_𝙾𝙡_πš…π™°π™»πš‚ are permutable.

  • Items of πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚ and πšƒπš„π™Ώπ™»π™΄πš‚_𝙾𝙡_πš…π™°π™»πš‚.πšπšžπš™πš•πšŽ are permutable (same permutation used).

  • All occurrences of two distinct tuples of values in πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚ or πšƒπš„π™Ώπ™»π™΄πš‚_𝙾𝙡_πš…π™°π™»πš‚.πšπšžπš™πš•πšŽ can be swapped; all occurrences of a tuple of values in πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚ or πšƒπš„π™Ώπ™»π™΄πš‚_𝙾𝙡_πš…π™°π™»πš‚.πšπšžπš™πš•πšŽ can be renamed to any unused tuple of values.

Usage

Quite often some constraints cannot be easily expressed, neither by a formula, nor by a regular pattern. In this case one has to define the constraint by specifying in extension the combinations of allowed values.

Remark

The πš’πš—_πš›πšŽπš•πšŠπšπš’πš˜πš— constraint is called πšŽπš‘πšπšŽπš—πšœπš’πš˜πš—πšŠπš•_πšœπšžπš™πš™πš˜πš›πš in JaCoP (http://www.jacop.eu/). Within SICStus Prolog the constraint can be applied to more than one single tuple of variables and is called πšπšŠπš‹πš•πšŽ. WithinΒ [BourdaisGalinierPesant03] this constraint is called πšŽπš‘πšπšŽπš—πšœπš’πš˜πš—.

Systems

feasPairAC in Choco, infeasPairAC in Choco, relationPairAC in Choco, feasTupleAC in Choco, infeasTupleAC in Choco, relationTupleAC in Choco, extensional in Gecode, extensionalsupportVA in JaCoP, extensionalsupportMDD in JaCoP, extensionalsupportSTR in JaCoP, case in SICStus, relation in SICStus, table in SICStus.

Used in

πšŒπš˜πš—πš_πš•πšŽπš‘_𝚌𝚘𝚜𝚝, πšŒπš˜πš—πš_πš•πšŽπš‘_πšπš›πšŽπšŠπšπšŽπš›, πšŒπš˜πš—πš_πš•πšŽπš‘_πšπš›πšŽπšŠπšπšŽπš›πšŽπšš, πšŒπš˜πš—πš_πš•πšŽπš‘_πš•πšŽπšœπšœ, πšŒπš˜πš—πš_πš•πšŽπš‘_πš•πšŽπšœπšœπšŽπšš.

See also

common keyword: πšŽπš•πšŽπš–πšŽπš—πšΒ (data constraint).

cost variant: πšŒπš˜πš—πš_πš•πšŽπš‘_𝚌𝚘𝚜𝚝 (π™²π™Ύπš‚πšƒ parameter added).

used in graph description: 𝚟𝚎𝚌_𝚎𝚚_πšπšžπš™πš•πšŽ.

Keywords

characteristic of a constraint: tuple, derived collection.

combinatorial object: relation.

constraint type: data constraint, extension.

filtering: arc-consistency.

Derived Collection
πšŒπš˜πš•πšƒπš„π™Ώπ™»π™΄πš‚_𝙾𝙡_πš…π™°πšπš‚-πšŒπš˜πš•πš•πšŽπšŒπšπš’πš˜πš—(𝚟𝚎𝚌-πšƒπš„π™Ώπ™»π™΄_𝙾𝙡_πš…π™°πšπš‚),πš’πšπšŽπš–(𝚟𝚎𝚌-πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚)]
Arc input(s)

πšƒπš„π™Ώπ™»π™΄πš‚_𝙾𝙡_πš…π™°πšπš‚ πšƒπš„π™Ώπ™»π™΄πš‚_𝙾𝙡_πš…π™°π™»πš‚

Arc generator
π‘ƒπ‘…π‘‚π·π‘ˆπΆπ‘‡β†¦πšŒπš˜πš•πš•πšŽπšŒπšπš’πš˜πš—(πšπšžπš™πš•πšŽπšœ_𝚘𝚏_πšŸπšŠπš›πšœ,πšπšžπš™πš•πšŽπšœ_𝚘𝚏_πšŸπšŠπš•πšœ)

Arc arity
Arc constraint(s)
𝚟𝚎𝚌_𝚎𝚚_πšπšžπš™πš•πšŽ(πšπšžπš™πš•πšŽπšœ_𝚘𝚏_πšŸπšŠπš›πšœ.𝚟𝚎𝚌,πšπšžπš™πš•πšŽπšœ_𝚘𝚏_πšŸπšŠπš•πšœ.πšπšžπš™πš•πšŽ)
Graph property(ies)
𝐍𝐀𝐑𝐂β‰₯1

Graph model

PartsΒ (A) andΒ (B) of FigureΒ 5.156.1 respectively show the initial and final graph associated with the Example slot. Since we use the 𝐍𝐀𝐑𝐂 graph property, the unique arc of the final graph is stressed in bold.

Figure 5.156.1. Initial and final graph of the πš’πš—_πš›πšŽπš•πšŠπšπš’πš˜πš— constraint
ctrs/in_relationActrs/in_relationB
(a) (b)