Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
The Design of the Zinc Modelling Language
Constraints
Efficient constraint propagation engines
ACM Transactions on Programming Languages and Systems (TOPLAS)
Propagation via lazy clause generation
Constraints
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
MiniZinc: towards a standard CP modelling language
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Nogood processing in csps
Revisiting the tree Constraint
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
A filter for the circuit constraint
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Using dominators for solving constrained path problems
PADL'06 Proceedings of the 8th international conference on Practical Aspects of Declarative Languages
CPAIOR'05 Proceedings of the Second international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Introducing global constraints in CHIP
Mathematical and Computer Modelling: An International Journal
ACSC '12 Proceedings of the Thirty-fifth Australasian Computer Science Conference - Volume 122
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The circuit constraint is used to constrain a graph represented by a successor for each node, such that the resulting edges form a circuit. Circuit and its variants are important for various kinds of tour-finding, path-finding and graph problems. In this paper we examine how to integrate the circuit constraint, and its variants, into a lazy clause generation solver. To do so we must extend the constraint to explain its propagation. We consider various propagation algorithms for circuit and examine how best to explain each of them. We compare the effectiveness of each propagation algorithm once we use explanation, since adding explanation changes the trade-off between propagation complexity and power. Simpler propagators, although less powerful, may produce more reusable explanations. Even though the most powerful propagator considered for circuit and variants creates huge explanations, we find that explanation is highly advantageous for solving problems involving this kind of constraint.