Singleton Consistencies

We perform a comprehensive theoretical and empirical study of the benefits of singleton consistencies. Our theoretical results help place singleton consistencies within the hierarchy of local consistencies. To determine the practical value of these theoretical results, we measured the cost-effectiveness of pre-processing with singleton consistency algorithms. Our experiments use both random and structured problems. Whilst pre-processing with singleton consistencies is not in general beneficial for random problems, it starts to pay off when randomness and structure are combined, and it is very worthwhile with structured problems like Golomb rulers. On such problems, pre-processing with consistency techniques as strong as singleton generalized arc-consistency (the singleton extension of generalized arc-consistency) can reduce runtimes. We also show that limiting algorithms that enforce singleton consistencies to a single pass often gives a small reduction in the amount of pruning and improves their cost-effectiveness. These experimental results also demonstrate that conclusions from studies on random problems should be treated with caution.