Abstract. The usual way for solving constraint satisfaction problems is to use a backtracking algorithm. One of the key factors in its e ciency is the rule it will use to decide on which v ariable to branch next (namely, the variable ordering heuristics). In this paper, we attempt to give a general formulation of dynamic variable ordering heuristics that take i n to account the properties of the neighborhood of the variable. An empirical evaluation on random CSPs and a sample of real instances shows that the obtained heuristics can improve signi cantly the current b e s t o n e s .
Recently, efficient algorithms have been proposed to achieve arc- and path-consistencey in constraint networks. For example, for arc-consistency, there are linear time algorithms (in the size of the problem) which are efficient in practice (e.g. AC-6 and AC-7). The best path-consistency algorithm proposed is PC-{5|6} which is a natural generalization of AC-6 to path-consistency. While its theoretical complexity is the best, experimentations show clearly that it is not very efficient in practice. In this paper, we propose two algorithms, one for arc-consistency, AC-8, and the second for path-consistency, PC-8. These algorithms are based on the same principle: to exploit minimal supports as AC-6 and PC-{5|6} do, but without recording them. While for AC-8, this approach is of limited interest, we show that for path-consistency, this new approach allows to outperform significantly existing algorithms.
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