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...

• Type: Conference
• Year: 2007
• Where: IJCAI
• Authors: Christophe Lecoutre, Fred Hemery
• Keywords: Artificial Intelligence, Basic Algorithm Ac3, IJCAI 2007, Multi-directional Residues, Smallest Current Support