5.45. balance_interval
DESCRIPTION | LINKS | GRAPH | AUTOMATON |
- Origin
- Constraint
- Arguments
- Restrictions
- Purpose
Consider the largest set (respectively the smallest set ) of variables of the collection that take their value in a same interval , where is an integer. is equal to the difference between the cardinality of and the cardinality of .
- Example
-
In the example, the third argument defines the following family of intervals , where is an integer. Values 6,4,3,3 and 4 are respectively located within intervals , , , and . Therefore intervals and are respectively used 1 and 4 times. The constraint holds since its first argument is assigned to the difference between the maximum and minimum number of the previous occurrences (i.e.,ย ).
- Typical
- Symmetries
Items of are permutable.
An occurrence of a value of that belongs to the -th interval, of size , can be replaced by any other value of the same interval.
- Arg. properties
Functional dependency: determined by and .
- Usage
An application of the constraint is to enforce a balanced assignment of interval of values, no matter how many distinct interval of values will be used. In this case one will push down the maximum value of the first argument of the constraint.
- See also
specialisation: ย ( replaced by ).
- Keywords
-
characteristic of a constraint: automaton, automaton with array of counters.
constraint arguments: pure functional dependency.
constraint type: value constraint.
final graph structure: equivalence.
modelling: interval, balanced assignment, functional dependency.
- Arc input(s)
- Arc generator
-
- Arc arity
- Arc constraint(s)
- Graph property(ies)
-
- Graph class
-
- Graph model
The graph property constraints the difference between the sizes of the largest and smallest strongly connected components.
Partsย (A) andย (B) of Figureย 5.45.1 respectively show the initial and final graph associated with the Example slot. Since we use the graph property, we show the largest and smallest strongly connected components of the final graph.
Figure 5.45.1. Initial and final graph of the constraint
(a) (b)
- Automaton
Figureย 5.45.2 depicts the automaton associated with the constraint. To each item of the collection corresponds a signature variable that is equal to 1.
Figure 5.45.2. Automaton of the constraint