DMCA
A study of residual supports in arc consistency (2007)
| Venue: | In Proceedings of IJCAI’07 |
| Citations: | 31 - 16 self |
BibTeX
@INPROCEEDINGS{Lecoutre07astudy,
author = {Christophe Lecoutre and Fred Hemery},
title = {A study of residual supports in arc consistency},
booktitle = {In Proceedings of IJCAI’07},
year = {2007},
pages = {125--130}
}
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Abstract
Abstract. 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 and MAC3rm admit a better worst-case time complexity than MAC2001 for a branch involving µ refutations when either µ> d 2 or µ> d and the tightness of any constraint is either low or high. Our experimental results clearly show that exploiting residues allows enhancing MAC and SAC algorithms. 1
Keyphrases
arc consistency residual support multi-directional residue well-known mac algorithm constraint network mac2001 present sac algorithm backtracking search current support worst-case time complexity domain size basic algorithm ac3 theoretical impact high constraint tightness binary tree previous execution experimental result uni-directional residue
