5.217. minimum
| DESCRIPTION | LINKS | GRAPH | AUTOMATON |
- Origin
CHIP
- Constraint
- Synonym
.
- Arguments
- Restrictions
- Purpose
is the minimum value of the collection of domain variables .
- Example
-
The constraint holds since its first argument is set to the minimum value of the collection .
- Symmetries
Items of are permutable.
All occurrences of two distinct values of can be swapped.
One and the same constant can be added to as well as to the attribute of all items of .
- Usage
In some project scheduling problems one has to introduce dummy activities that correspond for instance to the starting time of a given set of activities. In this context one can use the constraint to get the minimum starting time of a set of tasks.
- Remark
Note that is a constraint and not just a function that computes the minimum value of a collection of variables: potential values of influence the variables of , and reciprocally potential values that can be assigned to variables of influence .
The constraint is called in JaCoP (http://www.jacop.eu/).
- Algorithm
- Systems
min in Choco, min in Gecode, min in JaCoP, minimum in SICStus.
- Used in
- See also
common keyword: Β (order constraint).
generalisation: Β ( replaced by ).
implies: , .
soft variant: Β (value 0 is ignored), Β (open constraint).
specialisation: Β (minimum or order replaced by absolute minimum).
- Keywords
characteristic of a constraint: minimum, maxint, automaton, automaton without counters, reified automaton constraint.
constraint network structure: centered cyclic(1) constraint network(1).
- Arc input(s)
- Arc generator
-
- Arc arity
- Arc constraint(s)
- Graph property(ies)
-
- Graph model
The condition holds if and only if and corresponds to the same vertex. It is used in order to enforce to keep all the vertices of the initial graph. refers to the source vertices of the graph, i.e., those vertices that do not have any predecessor.
PartsΒ (A) andΒ (B) of FigureΒ 5.217.1 respectively show the initial and final graph associated with the Example slot. Since we use the graph property, the vertices of rank 0 (without considering the loops) of the final graph are outlined with a thick circle.
Figure 5.217.1. Initial and final graph of the constraint
(a) (b)
- Automaton
FigureΒ 5.217.2 depicts the automaton associated with the constraint. Let be the variable of the collection. To each pair corresponds a signature variable as well as the following signature constraint: .
Figure 5.217.2. Automaton of the constraint
Figure 5.217.3. Hypergraph of the reformulation corresponding to the automaton of the constraint
