Ordering heuristics for Singleton Arc Consistency

The use of consistency techniques is the main feature of any Constraint Satisfaction Problems(CSPs)solver. Arc Consistency (AC) applied to preprocessing can reduce the search space by removingthe values which are arc inconsistent. Singleton Arc Consistency (SAC) is a stronger level of consistencythan AC. Arc consistency technique with heuristic strategy has been proved to be an efficient techniqueto improve the efficiency of algorithms. In this paper, we first study the well-known SAC-3 algorithm indetail, and propose two algorithms with heuristic strategies for the drawbacks in SAC-3, SAC-3-FFPand SAC-3-MINIsup. Then, we give the correctness proof and complexity analysis. In the end, we implement the two algorithms in some random CSPs and benchmarks during the preprocessing step. Experimental results show that the two algorithms perform better than SAC-3 for most test cases.