- Origin
Arithmetic constraint.
- Constraint
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- Synonyms
,
,
,
.
- Arguments
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- Restrictions
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- Purpose
Constraint a linear term defined as the sum of products of coefficients and variables.
More precisely, let denote the sum of the product between a coefficient and its
variable of the different items of the collection.
Enforce the following constraint to hold: .
- Example
-
The constraint holds since the condition
is satisfied.
- Typical
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- Symmetries
Items of are permutable.
Attributes of are permutable w.r.t. permutation (permutation not necessarily applied to all items).
- Arg. properties
Contractible wrt. when , and .
Extensible wrt. when , and .
Aggregate: , , .
- Remark
The constraint is called in
Gecode
(http://www.gecode.org/).
It is called in
JaCoP
(http://www.jacop.eu/).
In the 2008 CSP solver competition the constraint
was called and required to be fixed.
- Algorithm
Most filtering algorithms first merge multiple occurrences of identical variables
in order to potentially make more deductions. When corresponds to
the less than or equal to constraint, a filtering algorithm achieving
bound-consistency for the
constraint with large numbers of variables
is described inΒ [HarveySchimpf02].
- Systems
equation in Choco,
linear in Gecode,
sumweight in JaCoP,
scalar_product in SICStus.
- See also
specialisation:
Β (arithmetic constraint where all coefficients are equal to 1).
- Keywords
characteristic of a constraint:
sum.
constraint type:
predefined constraint,
arithmetic constraint.
filtering:
duplicated variables.
