Decomposition Methods For Arbitrary Problems
The following methods can be used for translating an arbitrary constraint satisfaction problem, either binary or otherwise. Since they can also be used on binary problems, they can also be used on the result of making constraints binary, either by translating to the dual problem or by using hidden variables.
Some of these methods associate constraints with nodes of the tree, and define width taking into account the number of constraints associated with nodes. This may reduce the width of some problems. For example, a decomposition in which ten variables are associated with each node has width ten; however, if each of these sets of ten variables is the scope of a constraint, each node can be associated that constraint instead, resulting in width one.
Read more about this topic: Decomposition Method (constraint Satisfaction)
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