负表约束的简单表缩减广泛弧相容算法

Simple Tabular Reduction for Generalized Arc Consistency on Negative Table Constraints

广泛弧相容算法(generalized arc consistency,简称GAC),是求解约束满足问题的核心方法.表约束理论上可以表示所有约束关系,在过去10年中,有很多应用于表约束的广泛弧相容算法被提出来.在这些算法中,表缩减算法的效率非常高.但是目前的表缩减算法只能应用于正表约束,无法直接应用于负表约束.首先,提出一种表缩减算法STR-N,可以直接应用于负表约束;然后,给出了STR-N的两个改进版本STR-N2和STR-NIC.实验结果显示,STR-N算法在负表约束上的求解效率具有明显的优势.

Generalized arc consistency （GAC） plays a central role in solving the constraint satisfaction problem. Table constraints can theoretically represent all kinds of constraint relations, and many algorithms have been proposed to establish GAC on table constraints in the past decade. Among these methods, the simple tabular reduction algorithms （STR） are very efficient. However, the existing STR algorithms are suitable for only positive table constraints. They can not directly work on negative table constraints. In this paper, a STR algorithm, called STR-N, is first proposed to directly work on negative table constraints. Then, two improved versions of STR-N, STR-N2 and STR-NIC are presented. Experimental results show that the STR-N algorithms bring improvements over CPU time while solving the instances with negative table constraints.