关键词: 高阶相容, 极小约束范围, 约束网络, PW\+{sup}数据结构, PWC+GAC

Abstract: Table constraints, i.e., constraints given in extension by listing all allowed (or forbidden) tuples, are very straight forward and easy to understand, which are intensively studied in constraint programming (CP). Because such constraints are presented in many real world applications from areas such as design, databases, configuration and preferences modeling. However, With the growth of number of constraints and number of tuples, the space cost for table constraints and time cost of consistency checking have become key topics. eSTR is an algorithm which extends simple tabular reduction (STR) to higher-order consistency. After in-depth analysis of eSTR algorithm, this paper proposes two kinds of optimized methods for eSTR: PW\+{sup} data structure and minimal constraint scope, and then we prove that the constraint network enforce Pair-Wise Consistency and Generalized Arc-Consistency (PWC+GAC) with minimal constraint scope is equivalent to original constraint scope. At the same time, minimal constraint scope can reduce further space cost of eSTR2 algorithm by deleting columns of the tables in constraints, and PW\+{sup} data structure can reduce the CPU running time by avoiding some unnecessary checking of Pair-Wise-support (PW-support), since tuples in table of the constraint may not lose any PW-supports on the tables of other neighbour constraints. The experimental results show that combining our methods with eSTR2 algorithm can obviously outperform eSTR2 and eSTR2w on many instances of different problems, since it reduces the space cost and CPU running time of eSTR algorithm.

Key words: higher-order consistency, minimal constraint scope, constraint network, PW\+{sup} data structure, PWC+GAC