Cut-and-Traverse: A New Structural Decomposition Strategy for Finite Constraint Satisfaction Problems

In this paper, we propose a new heuristic structural decomposition strategy for Constraint Satisfaction Problems (CSPs), called Cut-and-Traverse (CAT) decomposition. This method has three steps: cutting step, traversing step and combining step. In the first step, cutting step, we gradually decompose the structure of a CSP instance to multiple partitions by finding independent cuts in a given CSP. Every cut is a set of hyperedges in a CSP instance. We can control the size of cut by only finding independent cuts that are no greater than a given bound number h. In the second step, traversing step, we traverse each partition and get an equivalent acyclic constraint network for each partition. In the third step, combining step, we combine the acyclic constraint networks in all partitions and get an equivalent acyclic constraint network for the given CSP. Using this method, the complexity is O(|E|) where |E| is the number of constraints in given CSP instance. Our experiment shows that CAT decomposition spends far much less time than hypertree decomposition while sometimes produces same hyperwidth decomposition as hypertree decomposition. Also it is shown that CAT decomposition always produces better decomposition result than hinge decomposition.