Network-based heuristics for constraint-satisfaction problems
Artificial Intelligence
Probabilistic reasoning in expert systems: theory and algorithms
Probabilistic reasoning in expert systems: theory and algorithms
Look-ahead techniques for micro-opportunistic job shop scheduling
Look-ahead techniques for micro-opportunistic job shop scheduling
Journal of the ACM (JACM)
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
Look-ahead value ordering for constraint satisfaction problems
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Where the really hard problems are
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
Bayes networks for estimating the number of solutions to a CSP
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
An Empirical Study of Probabilistic Arc Consistency
CP '02 Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming
Probabilistic Nogood Store as a Heuristic
PRICAI '08 Proceedings of the 10th Pacific Rim International Conference on Artificial Intelligence: Trends in Artificial Intelligence
Probabilistic arc consistency: a connection between constraint reasoning and probabilistic reasoning
UAI'00 Proceedings of the Sixteenth conference on Uncertainty in artificial intelligence
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Searching for solutions to constraint satisfaction problems (CSPs) is NP-hard in general. Heuristics for variable and value ordering have proven useful in guiding the sestrch towards more fruitful areas of the search space and hence reducing the amount of time spent searching for solutions. Static ordering methods impart an ordering in advance of the search and dynamic ordering methods use information about the state of the search to order values or variables during the search. A well-known static value ordering heuristic guides the search by ordering values based on an estimate of the number of solutions to the problem. This paper compares the performance of several such heuristics and shows that they do not give a significant improvement to a random ordering for hard CSPs. We give a dynamic ordering heuristic which decomposes the CSP into spanning trees and uses Bayesian networks to compute probabilistic approximations based on the current search state. Our empirical results show that this dynamic value ordering heuristic is an improvement for sparsely constrained CSPs and detects insoluble problem instances with fewer backtracks in many cases. However, as the problem density increases, our results show that the dynamic method and static methods do not significantly improve search performance.