Quick Shaving

Arc-consistency plays such a key role in constraint programming for solving real life problems that it is almost the only algorithm used for reducing domains. There are a few specific problems for which a stronger form of propagation, often called shaving, is more efficient. Nevertheless, in many cases. shaving at each node of the search tree is not worth doing: arc-consistency filtering is much faster, and the additional domain reductions inferred by shaving do not pay off. In this paper, we propose a new kind of shaving called QuickShaving, which is guided by the search. As QuickShaving may infer some additional domain reductions compared with arc-consistency, it can improve the search for a solution by an exponential ratio. Moreover, the advantage of Quick Shaving is that in practice, unlike a standard form of shaving, the additional domain reductions deduced by QuickShaving come at a very low overhead compared with arc-consistency.

[1]  Thomas C. Henderson,et al.  Arc and Path Consistency Revisited , 1986, Artif. Intell..

[2]  Yahia Lebbah,et al.  Acceleration methods of numeric CSPc , 1998, AAAI 1998.

[3]  Yahia Lebbah,et al.  Acceleration Methods for Numeric CSPs , 1998, AAAI/IAAI.

[4]  Christian Bliek,et al.  Generalizing Partial Order and Dynamic Backtracking , 1998, AAAI/IAAI.

[5]  Patrick Prosser,et al.  MAC-CBJ: maintaining arc consistency with conflict-directed backjumping , 1995 .

[6]  Christian Bessiere,et al.  Arc-Consistency and Arc-Consistency Again , 1993, Artif. Intell..

[7]  Roland H. C. Yap,et al.  Making AC-3 an Optimal Algorithm , 2001, IJCAI.

[8]  Roman Barták,et al.  A New Algorithm for Singleton Arc Consistency , 2004, FLAIRS.

[9]  Stuart A. Kauffman,et al.  ORIGINS OF ORDER , 2019, Origins of Order.

[10]  Matthew L. Ginsberg,et al.  Dynamic Backtracking , 1993, J. Artif. Intell. Res..

[11]  Christian Bessiere,et al.  Refining the Basic Constraint Propagation Algorithm , 2001, JFPLC.

[12]  Christian Bessiere,et al.  Some Practicable Filtering Techniques for the Constraint Satisfaction Problem , 1997, IJCAI.

[13]  Christian Bessiere,et al.  Arc Consistency for General Constraint Networks: Preliminary Results , 1997, IJCAI.

[14]  Matthew L. Ginsberg,et al.  GSAT and dynamic backtracking , 1994, KR 1994.

[15]  Gerald J. Sussman,et al.  Forward Reasoning and Dependency-Directed Backtracking in a System for Computer-Aided Circuit Analysis , 1976, Artif. Intell..

[16]  Christian Bessiere,et al.  Optimal and Suboptimal Singleton Arc Consistency Algorithms , 2005, IJCAI.

[17]  Olivier Lhomme,et al.  Consistency Techniques for Numeric CSPs , 1993, IJCAI.