Reasoning by Dominance in Not-Equals Binary Constraint Networks

Dynamic detection and elimination of symmetry in constraints, is in general a hard task, but in Not-Equals binary constraint networks, the symmetry conditions can be simplified. In this paper, we extend the principle of symmetry to dominance in Not-Equals Constraint Networks and show how dominated values are detected and eliminated at each node of the search tree. A Linear time complexity algorithm which detects the dominated values is proposed. Dominance is exploited in an enumerative method adapted to solve Not-Equals CSPs. This enumerative method augmented by Dominance is experimented on both randomly generated instances of graph coloring and Dimacs graph coloring benchmarks and its performance is compared to the same method augmented by symmetry and to the well known DSATUR method. The obtained results show that reasoning by dominance improves symmetry reasoning and our method outperforms both previous methods in solving graph coloring.