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摘要: 研究了求解约束满足问题(Constraint satisfaction problem, CSP)中的预处理技术. 首先提出了子论域上的完全独立相容性(Entirety singleton consistency, ESC)概念和相应算法, 分析并证明了算法的复杂性和正确性, 而后对其两条重要性质进行了详细证明. 基于此概念和性质, 提出了一种基于完全独立相容性的预处理算法: SAC-ESC算法, 并给出了正确性证明. 最后, 本文采用分治思想, 根据不同问题的论域自适应地合理划分其子论域. 实验结果表明, 对于随机问题、鸽巢问题、N皇后问题和基准用例, 算法SAC-ESC的执行效率大约是目前流行算法SAC-SDS和SAC-3的3~20倍.Abstract: This paper studies the technique of preprocessing in constraint satisfaction problem (CSP). Firstly, we propose a notion of entirety singleton consistency (ESC) and the algorithm, and then analyze the time and space complexity and correctness. Based on this, we present a new preprocessing algorithm SAC-ESC based on ESC, and prove its correctness. Furthermore, we use the divide-conquer strategy for the algorithm to automatically adapt to domain partition of various problems. In our experiments on random CSPs, pigeon problems, N-queens problems and benchmarks, the efficiency of our algorithm SAC-ESC is 3~20 times those of the existing SAC-SDS and SAC-3.
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