Decomposition method (constraint satisfaction): Difference between revisions

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In [[constraint satisfaction]], a '''decomposition method''' translates a [[constraint satisfaction problem]] into another constraint satisfaction problem that is binary and [[directed acyclic graph|acyclic]]. Decomposition methods work by grouping variables into sets, and solving a subproblem for each set. These translations are done because solving binary acyclic problems is a [[tractable problem]].
 
Each structural restriction defined a measure of complexity of solving the problem after conversion; this measure is called ''width''. Fixing a maximal allowed width is a way for identifying a subclass of constraint satisfaction problems. Solving problems in this class is polynomial for most decompositions; if this holds for a decomposition, the class of fixed-width problems form a tractable subclass of constraint satisfaction problems.