5.36. atleast
DESCRIPTION | LINKS | GRAPH | AUTOMATON |
- Origin
CHIP
- Constraint
- Synonym
.
- Arguments
- Restrictions
- Purpose
At least variables of the collection are assigned value .
- Example
-
The constraint holds since at least 2 values of the collection are equal to value 4.
- All solutions
FigureΒ 5.36.1 gives all solutions to the following non ground instance of the constraint: , , , , .
Figure 5.36.1. All solutions corresponding to the non ground example of the constraint of the All solutions slot
- Typical
- Symmetries
Items of are permutable.
can be decreased to any value .
An occurrence of a value of that is different from can be replaced by any other value.
- Arg. properties
Extensible wrt. .
- Systems
occurenceMin in Choco, count in Gecode, atleast in Gecode, count in JaCoP, at_least in MiniZinc, count in SICStus.
- Used in
- See also
common keyword: Β (value constraint).
implied by: Β ( replaced by ).
related: .
- Keywords
characteristic of a constraint: automaton, automaton with counters.
constraint network structure: alpha-acyclic constraint network(2).
- Arc input(s)
- Arc generator
-
- Arc arity
- Arc constraint(s)
- Graph property(ies)
-
- Graph model
Since each arc constraint involves only one vertex ( is fixed), we employ the arc generator in order to produce a graph with a single loop on each vertex.
PartsΒ (A) andΒ (B) of FigureΒ 5.36.2 respectively show the initial and final graph associated with the Example slot. Since we use the graph property, the loops of the final graph are stressed in bold.
Figure 5.36.2. Initial and final graph of the constraint
(a) (b)
- Automaton
FigureΒ 5.36.3 depicts the automaton associated with the constraint. To each variable of the collection corresponds a 0-1 signature variable . The following signature constraint links and : . The automaton counts the number of variables of the collection that are assigned value and finally checks that this number is greater than or equal to .
Figure 5.36.3. Automaton of the constraint
Figure 5.36.4. Hypergraph of the reformulation corresponding to the automaton (with one counter) of the constraint: since all states variables are fixed to the unique state of the automaton, the transitions constraints share only the counter variable and the constraint network is Berge-acyclic