Some decompositions use the number of variables of a node (or a similar amount) as the width. Others do not: cycle hypercutset, hinge decomposition, query decomposition, hypertree decomposition, and generalized hypertree decomposition associate constraints (or their scopes in form of hyperedges) with nodes, and include the number of constraints associated to a node in the width. This can be a significant save in terms of width. Indeed, problems with a single constraint on formula_23 variables can only be decomposed in a tree with a single node. This node can be associated with the formula_23 variables or with the single constraint. Counting the number of variables leads to width formula_23, while counting the number of constraints leads to width formula_26.