TY - JOUR
T1 - An optimal coarse-grained arc consistency algorithm
AU - Bessière, Christian
AU - Régin, Jean Charles
AU - Yap, Roland H.C.
AU - Zhang, Yuanlin
N1 - Funding Information:
✩ Preliminary versions of this paper appeared in [C. Bessière, J. Régin, in: Proc. IJCAI-01, Seattle, WA, 2001, pp. 309–315 [1]; Y. Zhang, R. Yap, in: Proc. IJCAI-01, Seattle, WA, 2001, pp. 316–321 [2]]. ✩✩ During this work, Christian Bessière was supported by ILOG under a research collaboration contract ILOG/CNRS/University of Montpelier II, Yuanlin Zhang by the Science Foundation Ireland under Grant 00/PI.1/C075, at the Cork Constraint Computation Centre, Computer Science Department, University College Cork, and Roland Yap and Yuanlin Zhang by the Academic Research Fund, National University of Singapore. * Corresponding author. E-mail addresses: bessiere@lirmm.fr (C. Bessière), regin@ilog.fr (J.-C. Régin), ryap@comp.nus.edu.sg (R.H.C. Yap), yzhang@cs.ttu.edu (Y. Zhang).
PY - 2005/7
Y1 - 2005/7
N2 - The use of constraint propagation is the main feature of any constraint solver. It is thus of prime importance to manage the propagation in an efficient and effective fashion. There are two classes of propagation algorithms for general constraints: fine-grained algorithms where the removal of a value for a variable will be propagated to the corresponding values for other variables, and coarse-grained algorithms where the removal of a value will be propagated to the related variables. One big advantage of coarse-grained algorithms, like AC-3, over fine-grained algorithms, like AC-4, is the ease of integration when implementing an algorithm in a constraint solver. However, fine-grained algorithms usually have optimal worst case time complexity while coarse-grained algorithms do not. For example, AC-3 is an algorithm with non-optimal worst case complexity although it is simple, efficient in practice, and widely used. In this paper we propose a coarse-grained algorithm, AC2001/3.1, that is worst case optimal and preserves as much as possible the ease of its integration into a solver (no heavy data structure to be maintained during search). Experimental results show that AC2001/3.1 is competitive with the best fine-grained algorithms such as AC-6. The idea behind the new algorithm can immediately be applied to obtain a path consistency algorithm that has the best-known time and space complexity. The same idea is then extended to non-binary constraints.
AB - The use of constraint propagation is the main feature of any constraint solver. It is thus of prime importance to manage the propagation in an efficient and effective fashion. There are two classes of propagation algorithms for general constraints: fine-grained algorithms where the removal of a value for a variable will be propagated to the corresponding values for other variables, and coarse-grained algorithms where the removal of a value will be propagated to the related variables. One big advantage of coarse-grained algorithms, like AC-3, over fine-grained algorithms, like AC-4, is the ease of integration when implementing an algorithm in a constraint solver. However, fine-grained algorithms usually have optimal worst case time complexity while coarse-grained algorithms do not. For example, AC-3 is an algorithm with non-optimal worst case complexity although it is simple, efficient in practice, and widely used. In this paper we propose a coarse-grained algorithm, AC2001/3.1, that is worst case optimal and preserves as much as possible the ease of its integration into a solver (no heavy data structure to be maintained during search). Experimental results show that AC2001/3.1 is competitive with the best fine-grained algorithms such as AC-6. The idea behind the new algorithm can immediately be applied to obtain a path consistency algorithm that has the best-known time and space complexity. The same idea is then extended to non-binary constraints.
KW - Arc consistency
KW - Constraint networks
KW - Constraint programming systems
KW - Non-binary constraints
KW - Path consistency
UR - http://www.scopus.com/inward/record.url?scp=18944390206&partnerID=8YFLogxK
U2 - 10.1016/j.artint.2005.02.004
DO - 10.1016/j.artint.2005.02.004
M3 - Article
AN - SCOPUS:18944390206
SN - 0004-3702
VL - 165
SP - 165
EP - 185
JO - Artificial Intelligence
JF - Artificial Intelligence
IS - 2
ER -