This decomposition method is based on the idea that, after some variables are given a value, what remains of the problem once these variables have been eliminated may be acyclic. Formally, a cycle cutset of a graph is a set of nodes that makes the graph acyclic when they are removed from it. A similar definition can be given for a constraint satisfaction problem using its primal graph. The width of a cycle decomposition is the number of variables in the cutset. The width of a problem is the minimal width of its cycle cutset decompositions.