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Global Constraint Catalogue: Past, Present and Future
, 2006
"... The catalogue of global constraints is reviewed, focusing on the graphbased description of global constraints. A number of possible enhancements are proposed as well as several research paths for the development of the area. ..."
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Cited by 10 (0 self)
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The catalogue of global constraints is reviewed, focusing on the graphbased description of global constraints. A number of possible enhancements are proposed as well as several research paths for the development of the area.
On Global Warming (Softening Global Constraints)
 In Proc. of the 6th International Workshop on Preferences and Soft Constraints
, 2004
"... We describe soft versions of the global cardinality constraint and the regular constraint, with e#cient filtering algorithms maintaining domain consistency. For both constraints, the softening is achieved by augmenting the underlying graph. The softened constraints can be used to extend the meta ..."
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Cited by 9 (1 self)
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We describe soft versions of the global cardinality constraint and the regular constraint, with e#cient filtering algorithms maintaining domain consistency. For both constraints, the softening is achieved by augmenting the underlying graph. The softened constraints can be used to extend the metaconstraint framework for overconstrained problems proposed by Petit, Regin and Bessiere.
Set Variables and Local Search
"... Many combinatorial (optimisation) problems have natural models based on, or including, set variables and set constraints. This modelling device has been around for quite some time in the constraint programming area, and proved its usefulness in many applications. This paper introduces set variable ..."
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Cited by 6 (6 self)
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Many combinatorial (optimisation) problems have natural models based on, or including, set variables and set constraints. This modelling device has been around for quite some time in the constraint programming area, and proved its usefulness in many applications. This paper introduces set variables and set constraints also in the local search area. It presents a way of representing set variables in the local search context, where we deal with concepts like transition functions, neighbourhoods, and penalty costs. Furthermore, some common set constraints and their penalty costs are defined. These constraints are later used to model three problems and some initial experimental results are reported.
Soft Constraints of Difference and Equality
"... In many combinatorial problems one may need to model the diversity or similarity of sets of assignments. For example, one may wish to maximise or minimise the number of distinct values in a solution. To formulate problems of this type we can use soft variants of the well known AllDifferent and AllEq ..."
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In many combinatorial problems one may need to model the diversity or similarity of sets of assignments. For example, one may wish to maximise or minimise the number of distinct values in a solution. To formulate problems of this type we can use soft variants of the well known AllDifferent and AllEqual constraints. We present a taxonomy of six soft global constraints, generated by combining the two latter ones and the two standard cost functions, which are either maximised or minimised. We characterise the complexity of achieving arc and bounds consistency on these constraints, resolving those cases for which NPhardness was neither proven nor disproven. In particular, we explore in depth the constraint ensuring that at least k pairs of variables have a common value. We show that achieving arc consistency is NPhard, however bounds consistency can be achieved in polynomial time through dynamic programming. Moreover, we show that the maximum number of pairs of equal variables can be approximated by a factor of 1 2 with a linear time greedy algorithm. Finally, we provide a fixed parameter tractable algorithm with respect to the number of values appearing in more than two distinct domains. Interestingly, this taxonomy shows that enforcing equality is harder than enforcing difference. 1.