Introduction to algorithms
Solution of large-scale symmetric travelling salesman problems
Mathematical Programming: Series A and B
An additive bounding procedure for the asymmetric travelling salesman problem
Mathematical Programming: Series A and B
Verification and sensitivity analysis of minimum spanning trees in linear time
SIAM Journal on Computing
A filtering algorithm for constraints of difference in CSPs
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Exact solution of large-scale, asymmetric traveling salesman problems
ACM Transactions on Mathematical Software (TOMS)
Applications of Path Compression on Balanced Trees
Journal of the ACM (JACM)
A minimum spanning tree algorithm with inverse-Ackermann type complexity
Journal of the ACM (JACM)
Embedding Relaxations in Global Constraints for Solving TSP and TSPTW
Annals of Mathematics and Artificial Intelligence
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
Reduced Cost-Based Ranking for Generating Promising Subproblems
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
SCIL - Symbolic Constraints in Integer Linear Programming
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
A Hybrid Exact Algorithm for the TSPTW
INFORMS Journal on Computing
Cardinal: A Finite Sets Constraint Solver
Constraints
Discrepancy-Based Additive Bounding Procedures
INFORMS Journal on Computing
The Traveling Salesman Problem: A Computational Study (Princeton Series in Applied Mathematics)
The Traveling Salesman Problem: A Computational Study (Princeton Series in Applied Mathematics)
The "Not-Too-Heavy Spanning Tree" Constraint
CPAIOR '07 Proceedings of the 4th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Revisiting the tree Constraint
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
The minimum spanning tree constraint
CP'06 Proceedings of the 12th 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
CPAIOR'05 Proceedings of the Second international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
The weighted spanning tree constraint revisited
CPAIOR'10 Proceedings of the 7th 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
Transforming asymmetric into symmetric traveling salesman problems
Operations Research Letters
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We study the weighted circuit constraint in the context of constraint programming. It appears as a substructure in many practical applications, particularly routing problems. We propose a domain filtering algorithm for the weighted circuit constraint that is based on the 1-tree relaxation of Held and Karp. In addition, we study domain filtering based on an additive bounding procedure that combines the 1-tree relaxation with the assignment problem relaxation. Experimental results on Traveling Salesman Problem instances demonstrate that our filtering algorithms can dramatically reduce the problem size. In particular, the search tree size and solving time can be reduced by several orders of magnitude, compared to existing constraint programming approaches. Moreover, for medium-size problem instances, our method is competitive with the state-of-the-art special-purpose TSP solver Concorde.