Analysis of three algorithms for finding all consistent labelings

Three algorithms for solving constraint satisfaction problems (CSPs) are compared analytically and experimentally. They are regular backtracking, R. Seidel´s (1981) invasion procedure and D. Waltz´s (1975) filtering algorithm. Each algorithm has been implemented in Prolog and used to solve several constraint satisfaction problems. It is observed analytically that regular backtracking requires an exponential running time while using only a linear amount of space, whereas the invasion algorithm invests more heavily in space in order to reduce the running time. The worst-case complexity of Waltz´s procedure is linear in the number of variables for both time required and space used. The experimental results suggest that regular backtracking performs reasonably well when the problem size is small. Both Waltz´s procedure and Seidel´s invasion algorithm seem to perform well when the CSP can be represented by a planar constraint graph, and hence should be efficient for vision applications. Seidel´s invasion algorithm can solve CSPs with constraints involving more than two variables