Arc-Consistency and Arc-Consistency Again

Christian Bessière, Marie-Odile Cordier

Constraint networks are known as a useful way to formulate problems such as design, scene labeling, temporal reasoning, and more recently natural language parsing. The problem of the existence of solutions in a constraint network is NP-complete. Hence, consistency techniques have been widely studied to simplify constraint networks before or during the search of solutions. Arc-consistency is the most used of them. Mohr and Henderson have proposed AC-4, an algorithm having an optimal worst-case time complexity. But it has two drawbacks: its space complexity and its average time complexity. In problems with many solutions, where the size of the constraints is large, these drawbacks become so important that users often replace AC-4 by AC-3, a non-optimal algorithm. In this paper, we propose a new algorithm, AC-6, which keeps the optimal worst-case time complexity of AC-4 while working out the drawback of space complexity. More, the average time complexity of AC-6 is optimal for constraint networks where nothing is known about the semantic of the constraints. At the end of the paper, experimental results show how much AC-6 outperforms AC-3 and AC-4.

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