On the Space-Time Trade-off in Solving Constraint Satisfaction Problems

A common technique for bounding the runtime required to solve a constraint satisfaction problem is to exploit the structure of the problem's constraint graph [Dechter, 92]. We show that a simple structure-based technique with a minimal space requirement, pseudo-tree search [Freuder & Quinn, 85], is capable of bounding runtime almost as effectively as the best exponential space-consuming schemes. Specifically, if we let n denote the number of variables in the problem, w* denote the exponent in the complexity function of the best structure-based techniques, and h denote the exponent from pseudotree search, we show h < {w* + 1) (lg(n) + 1) . The result should allow reductions in the amount of real-time accessible memory required for predicting runtime when solving CSP equivalent problems.