5.153. in_interval

DESCRIPTIONLINKSGRAPHAUTOMATON
Origin

Domain definition.

Constraint

πš’πš—_πš’πš—πšπšŽπš›πšŸπšŠπš•(πš…π™°πš,π™»π™Ύπš†,πš„π™Ώ)

Synonyms

πšπš˜πš–, πš’πš—.

Arguments
πš…π™°πšπšπšŸπšŠπš›
π™»π™Ύπš†πš’πš—πš
πš„π™Ώπš’πš—πš
Restriction
π™»π™Ύπš†β‰€πš„π™Ώ
Purpose

Enforce the domain variable πš…π™°πš to take a value within the interval [π™»π™Ύπš†,πš„π™Ώ].

Example
(3,2,5)

The πš’πš—_πš’πš—πšπšŽπš›πšŸπšŠπš• constraint holds since its first argument πš…π™°πš=3 is greater than or equal to its second argument π™»π™Ύπš†=2 and less than or equal to its third argument πš„π™Ώ=5.

Typical
π™»π™Ύπš†<πš„π™Ώ
πš…π™°πš>π™»π™Ύπš†
πš…π™°πš<πš„π™Ώ
Symmetries
  • π™»π™Ύπš† can be decreased.

  • πš„π™Ώ can be increased.

  • An occurrence of a value of πš…π™°πš can be replaced by any other value in [π™»π™Ύπš†,πš„π™Ώ].

  • One and the same constant can be added to πš…π™°πš, π™»π™Ύπš† and πš„π™Ώ.

Remark

Entailment occurs immediately after posting this constraint.

The πš’πš—_πš’πš—πšπšŽπš›πšŸπšŠπš• constraint is referenced under the name πšπš˜πš– inΒ Gecode.

Systems

member in Choco, in in JaCoP, in in SICStus.

See also

common keyword: πšπš˜πš–πšŠπš’πš—, πš’πš—Β (domain definition).

generalisation: πš’πš—_πš’πš—πšπšŽπš›πšŸπšŠπš•_πš›πšŽπš’πšπš’πšŽπšΒ (reified version), πš’πš—_πš’πš—πšπšŽπš›πšŸπšŠπš•πšœΒ (single interval replaced by a set of intervals), πš’πš—_𝚜𝚎𝚝 (interval replaced by set variable).

Keywords

characteristic of a constraint: automaton, automaton without counters, reified automaton constraint, derived collection.

constraint arguments: unary constraint.

constraint network structure: Berge-acyclic constraint network.

constraint type: value constraint.

filtering: arc-consistency.

modelling: interval, domain definition.

Derived Collections
πšŒπš˜πš•(πš…π™°πšπ™Έπ™°π™±π™»π™΄-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š’πšπšŽπš–(πšŸπšŠπš›-πš…π™°πš)])
πšŒπš˜πš•π™Έπ™½πšƒπ™΄πšπš…π™°π™»-πšŒπš˜πš•πš•πšŽπšŒπšπš’πš˜πš—(πš•πš˜πš -πš’πš—πš,πšžπš™-πš’πš—πš),πš’πšπšŽπš–(πš•πš˜πš -π™»π™Ύπš†,πšžπš™-πš„π™Ώ)]
Arc input(s)

πš…π™°πšπ™Έπ™°π™±π™»π™΄ π™Έπ™½πšƒπ™΄πšπš…π™°π™»

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šŸπšŠπš›πš’πšŠπš‹πš•πšŽ,πš’πš—πšπšŽπš›πšŸπšŠπš•)

Arc arity
Arc constraint(s)
β€’ πšŸπšŠπš›πš’πšŠπš‹πš•πšŽ.πšŸπšŠπš›β‰₯πš’πš—πšπšŽπš›πšŸπšŠπš•.πš•πš˜πš 
β€’ πšŸπšŠπš›πš’πšŠπš‹πš•πšŽ.πšŸπšŠπš›β‰€πš’πš—πšπšŽπš›πšŸπšŠπš•.πšžπš™
Graph property(ies)
𝐍𝐀𝐑𝐂=1

Graph model

PartsΒ (A) andΒ (B) of FigureΒ 5.153.1 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 5.153.1. Initial and final graph of the πš’πš—_πš’πš—πšπšŽπš›πšŸπšŠπš• constraint
ctrs/in_intervalActrs/in_intervalB
(a) (b)
Automaton

FigureΒ 5.153.2 depicts the automaton associated with the πš’πš—_πš’πš—πšπšŽπš›πšŸπšŠπš• constraint. We have one single 0-1 signature variable πš‚ as well as the following signature constraint: πš…π™°πšβ‰₯π™»π™Ύπš†βˆ§πš…π™°πšβ‰€πš„π™Ώβ‡”πš‚.

Figure 5.153.2. Automaton of the πš’πš—_πš’πš—πšπšŽπš›πšŸπšŠπš• constraint
ctrs/in_interval1
Figure 5.153.3. Hypergraph of the reformulation corresponding to the automaton of the πš’πš—_πš’πš—πšπšŽπš›πšŸπšŠπš• constraint
ctrs/in_interval2