Data Structures for Generalised Arc Consistency for Extensional Constraints

Extensional (table) constraints are an important tool for attacking combinatorial problems with constraint programming. Recently there has been renewed interest in fast propagation algorithms for these constraints. We describe the use of two alternative data structures for maintaining generalised arc consistency on extensional constraints. The first, the Next-Difference list, is novel and has been developed with this application in mind. The second, the trie, is well known but its use in this context is novel. Empirical analyses demonstrate the efficiency of the resulting approaches, both in GAC-schema, and in the watched-literal table constraint in Minion.

[1]  Edward Fredkin,et al.  Trie memory , 1960, Commun. ACM.

[2]  Mark E. Stickel,et al.  Implementing the Davis–Putnam Method , 2000, Journal of Automated Reasoning.

[3]  Ian P. Gent,et al.  Minion: A Fast Scalable Constraint Solver , 2006, ECAI.

[4]  Christophe Lecoutre,et al.  Generalized Arc Consistency for Positive Table Constraints , 2006, CP.

[5]  Toby Walsh,et al.  Propagation algorithms for lexicographic ordering constraints , 2006, Artif. Intell..

[6]  Alan K. Mackworth.  On Reading Sketch Maps , 1977, IJCAI.

[7]  Mark Wallace,et al.  Practical applications of constraint programming , 2004, Constraints.

[8]  Toby Walsh,et al.  Using Auxiliary Variables and Implied Constraints to Model Non-Binary Problems , 2000, AAAI/IAAI.

[9]  Jean-Charles Régin,et al.  A Filtering Algorithm for Constraints of Difference in CSPs , 1994, AAAI.

[10]  Ian P. Gent,et al.  Watched Literals for Constraint Propagation in Minion , 2006, CP.

[11]  Roland H. C. Yap,et al.  An optimal coarse-grained arc consistency algorithm , 2005, Artif. Intell..

[12]  Philippe Baptiste,et al.  Constraint Propagation and Decomposition Techniques for Highly Disjunctive and Highly Cumulative Project Scheduling Problems , 1997, Constraints.

[13]  Jean-Charles Régin,et al.  A Fast Arc Consistency Algorithm for n-ary Constraints , 2005, AAAI.

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

[15]  Alan M. Frisch,et al.  Symmetry and Implied Constraints in the Steel Mill Slab Design Problem , 2001 .

[16]  Roland H. C. Yap,et al.  Maintaining Generalized Arc Consistency on Ad-Hoc n-Ary Boolean Constraints , 2006, ECAI.