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Artificial Intelligence - Chips challenging champions: games, computers and Artificial Intelligence
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Constraints
Beyond NP: Arc-Consistency for Quantified Constraints
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Artificial Intelligence: A Modern Approach
Artificial Intelligence: A Modern Approach
Solving weighted CSP by maintaining arc consistency
Artificial Intelligence
Principles of Constraint Programming
Principles of Constraint Programming
Algorithmic Game Theory
Quantified Constraint Optimization
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
CSP properties for quantified constraints: definitions and complexity
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
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
QCSP-solve: a solver for quantified constraint satisfaction problems
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Soft arc consistency revisited
Artificial Intelligence
Modeling Soft Global Constraints as Linear Programs in Weighted Constraint Satisfaction
ICTAI '11 Proceedings of the 2011 IEEE 23rd International Conference on Tools with Artificial Intelligence
Weighted Constraint Satisfaction Problems with Min-Max Quantifiers
ICTAI '11 Proceedings of the 2011 IEEE 23rd International Conference on Tools with Artificial Intelligence
Journal of Artificial Intelligence Research
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Minimax Weighted Constraint Satisfaction Problems (formerly called Quantified Weighted CSPs) are a framework for modeling soft constrained problems with adversarial conditions. In this paper, we describe novel definitions and implementations of node, arc and full directional arc consistency notions to help reduce search space on top of the basic tree search with alpha-beta pruning for solving ultra-weak solutions. In particular, these consistencies approximate the lower and upper bounds of the cost of a problem by exploiting the semantics of the quantifiers and reusing techniques from both Weighted and Quantified CSPs. Lower bound computation employs standard estimation of costs in the sub-problems used in alpha-beta search. In estimating upper bounds, we propose two approaches based on the Duality Principle: duality of quantifiers and duality of constraints. The first duality amounts to changing quantifiers from min to max , while the second duality re-uses the lower bound approximation functions on dual constraints to generate upper bounds. Experiments on three benchmarks comparing basic alpha-beta pruning and the six consistencies from the two dualities are performed to confirm the feasibility and efficiency of our proposal.