The '''dual problem''' is a reformulation of a [[constraint satisfaction problem]] expressing each constraint of the original problem as a variable. Dual problems only contain [[binary constraintsconstraint]]s, and are therefore solvable by [[algorithm]]s tailored for such problems. The '''join graphs''' and '''join trees''' of a constraint satisfaction problem are [[Graph (graph theory)|graph]]s representing its dual problem or a problem obtained from the dual problem removing some redundant constraints.
