Two new constraint propagation algorithms requiring small space complexity

Recently, efficient algorithms have been proposed to achieve arc- and path-consistency in constraint networks. The best path-consistency algorithm proposed is PE-{5|6} which is a natural generalization of AC-6 to path-consistency independently proposed by M. Singh (1995) for PC-5 and A. Chmeiss and P. Jegou (1995) for PC-6. Unfortunately, we have remarked that PC-{5|6}, though it is widely better than PC-4 (Chmeiss and P. Jegou, 1996) was not very efficient in practice, especially for those classes of problems that require an important space to be run. So, we propose a new path-consistency algorithm called PC-8, the space complexity of which is O(n²d) but its time complexity is O(n³d⁴), i.e. worse than that of PC-{5|6}. However, the simplicity of PC-8 as well as the data structures used for its implementation offer a higher performance than PC-{5|6}. The principle of PC-8 is also used to propose a new algorithm to achieve arc-consistency called AC-8.