A Study of Residual Supports in Arc Consistency

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A Study of Residual Supports in Arc Consistency
In an Arc Consistency (AC) algorithm, a residual support, or residue, is a support that has been stored during a previous execution of the procedure which determines if a value is supported by a constraint. The point is that a residue is not guaranteed to represent a lower bound of the smallest current support of a value. In this paper, we study the theoretical impact of exploiting residues with respect to the basic algorithm AC3. First, we prove that AC3r (AC3 with uni-directional residues) and AC3rm (AC3 with multi-directional residues) are optimal for low and high constraint tightness. Second, we show that when AC has to be maintained during a backtracking search (the well-known MAC algorithm), MAC2001 presents, with respect to MAC3r and MAC3rm, an overhead in O(µed) per branch of the binary tree built by MAC, where µ denotes the number of refutations of the branch, e the number of constraints and d the greatest domain size of the constraint network. One consequence is that, MAC3r...
Christophe Lecoutre, Fred Hemery
Added 29 Oct 2010
Updated 29 Oct 2010
Type Conference
Year 2007
Authors Christophe Lecoutre, Fred Hemery
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