5.130. distance_between
DESCRIPTION | LINKS | GRAPH |
- Origin
N.Β Beldiceanu
- Constraint
- Synonym
.
- Arguments
- Restrictions
- Purpose
Let and be respectively the and variables of the collection . In a similar way, let and be respectively the and variables of the collection . is equal to the number of times one of the following mutually incompatible conditions are true:
holds and does not hold,
holds and does not hold.
- Example
-
The constraint holds since the following conditions are verified:
- Typical
- Symmetries
Arguments are permutable w.r.t. permutation .
Items of and are permutable (same permutation used).
One and the same constant can be added to the attribute of all items of .
One and the same constant can be added to the attribute of all items of .
- Arg. properties
Functional dependency: determined by , and .
- Usage
Measure the distance between two sequences in term of the number of constraint changes. This should be put in contrast to the number of value changes that is sometimes superficial.
- See also
- Keywords
constraint arguments: pure functional dependency.
- Arc input(s)
/
- Arc generator
-
- Arc arity
- Arc constraint(s)
- Graph property(ies)
-
- Graph model
Within the Arc input(s) slot, the character / indicates that we generate two distinct graphs. The graph property measures the distance between two digraphs and . This distance is defined as the sum of the following quantities:
The number of arcs of that do not belong to ,
The number of arcs of that do not belong to .
PartΒ (A) of FigureΒ 5.130.1 gives the final graph associated with the sequence -3,-4,-6,-2,-4 (i.e.,Β the second argument of the constraint of the Example slot), while partΒ (B) shows the final graph corresponding to -2,-6,-9,-3,-6 (i.e.,Β the third argument of the constraint of the Example slot). The two arc constraints that differ from one graph to the other are marked by a dotted line. The constraint holds since between sequence -3,-4,-6,-2,-4 and sequence -2,-6,-9,-3,-6 there are changes that respectively correspond to:
Within the final graph associated with sequence -3,-4,-6,-2,-4 the arc (i.e.,Β values ) does not occur in the final graph associated with -2,-6,-9,-3,-6,
Within the final graph associated with sequence -2,-6,-9,-3,-6 the arc (i.e.,Β values ) does not occur in the final graph associated with -3,-4,-6,-2,-4.
Figure 5.130.1. Final graphs of the constraint
(a) (b)