Maintaining arc consistency algorithms during the search without additional space cost

Abstract

In this paper, we detail the versions of the arc consistency algorithms for binary constraints based on list of supports and last value when they are maintained during the search for solutions. In other words, we give the explicit codes of MAC-6 and MAC-7 algorithms. Moreover, we present an original way to restore the last values of AC-6 and AC-7 algorithms in order to obtain a MAC version of these algorithms whose space complexity remains in O(ed) while keeping the O(ed2) time complexity on any branch of the tree search, where d is the size of the largest domain and e is the number of constraints. This result outperforms all previous studies. © Springer-Verlag Berlin Heidelberg 2005.