Efficient Algorithms for Shortest Paths in Sparse Networks
Journal of the ACM (JACM)
PPDP '99 Proceedings of the International Conference PPDP'99 on Principles and Practice of Declarative Programming
CP '02 Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming
A Filtering Algorithm for the Stretch Constraint
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Specific Filtering Algorithms for Over-Constrained Problems
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Meta-constraints on violations for over constrained problems
ICTAI '00 Proceedings of the 12th IEEE International Conference on Tools with Artificial Intelligence
Arc consistency for soft constraints
Artificial Intelligence
Solving weighted CSP by maintaining arc consistency
Artificial Intelligence
On global warming: Flow-based soft global constraints
Journal of Heuristics
Flow-Based Propagators for the SEQUENCE and Related Global Constraints
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Valued constraint satisfaction problems: hard and easy problems
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
In the quest of the best form of local consistency for weighted CSP
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Bounds arc consistency for weighted CSPs
Journal of Artificial Intelligence Research
Existential arc consistency: getting closer to full arc consistency in weighted CSPs
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Soft arc consistency revisited
Artificial Intelligence
Generalized arc consistency for global cardinality constraint
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
A nurse rostering system using constraint programming and redundant modeling
IEEE Transactions on Information Technology in Biomedicine
Consistencies for ultra-weak solutions in minimax weighted CSPs using the duality principle
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
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Many combinatorial problems deal with preferences and violations, the goal of which is to find solutions with the minimum cost. Weighted constraint satisfaction is a framework for modeling such problems, which consists of a set of cost functions to measure the degree of violation or preferences of different combinations of variable assignments. Typical solution methods for weighted constraint satisfaction problems (WCSPs) are based on branch-and-bound search, which are made practical through the use of powerful consistency techniques such as AC*, FDAC*, EDAC* to deduce hidden cost information and value pruning during search. These techniques, however, are designed to be efficient only on binary and ternary cost functions which are represented in table form. In tackling many real-life problems, high arity (or global) cost functions are required. We investigate efficient representation scheme and algorithms to bring the benefits of the consistency techniques to also high arity cost functions, which are often derived from hard global constraints from classical constraint satisfaction. The literature suggests some global cost functions can be represented as flow networks, and the minimum cost flow algorithm can be used to compute the minimum costs of such networks in polynomial time. We show that naive adoption of this flow-based algorithmic method for global cost functions can result in a stronger form of ?-inverse consistency. We further show how the method can be modified to handle cost projections and extensions to maintain generalized versions of AC* and FDAC* for cost functions with more than two variables. Similar generalization for the stronger EDAC* is less straightforward. We reveal the oscillation problem when enforcing EDAC* on cost functions sharing more than one variable. To avoid oscillation, we propose a weak version of EDAC* and generalize it to weak EDGAC* for non-binary cost functions. Using various benchmarks involving the soft variants of hard global constraints ALLDIFFERENT, GCC, SAME, and REGULAR, empirical results demonstrate that our proposal gives improvements of up to an order of magnitude when compared with the traditional constraint optimization approach, both in terms of time and pruning.