5.259. min_size_set_of_consecutive_var
DESCRIPTION | LINKS | GRAPH |
- Origin
N.Β Beldiceanu
- Constraint
- Arguments
- Restrictions
- Purpose
is the size of the smallest set of variables of the collection that all take their value in a set of consecutive values.
- Example
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In the first example, the two parts and take respectively their values in the two following sets of consecutive values and . Consequently, the corresponding constraint holds since the cardinality of the smallest set of variables is 4.
- Typical
- Symmetries
Items of are permutable.
All occurrences of two distinct values of can be swapped.
One and the same constant can be added to the attribute of all items of .
- Arg. properties
Functional dependency: determined by .
- Counting
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Length () 2 3 4 5 6 7 8 Solutions 9 64 625 7776 117649 2097152 43046721 Number of solutions for : domains
Length () 2 3 4 5 6 7 8 Total 9 64 625 7776 117649 2097152 43046721 Parameter value 1 2 30 276 3580 57000 1065834 22894984 2 7 - 132 2480 30990 522522 11080412 3 - 34 - - 13500 332430 4590208 4 - - 217 - - - 2293480 5 - - - 1716 - - - 6 - - - - 16159 - - 7 - - - - - 176366 - 8 - - - - - - 2187637 Solution count for : domains
- See also
- Keywords
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characteristic of a constraint: consecutive values, minimum.
constraint arguments: pure functional dependency.
- Arc input(s)
- Arc generator
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- Arc arity
- Arc constraint(s)
- Graph property(ies)
-
- Graph model
Since the arc constraint is symmetric each strongly connected component of the final graph corresponds exactly to one connected component of the final graph.
PartsΒ (A) andΒ (B) of FigureΒ 5.259.1 respectively show the initial and final graph associated with the first example of the Example slot. Since we use the graph property, we show the smallest strongly connected component of the final graph.
Figure 5.259.1. Initial and final graph of the constraint
(a) (b)