A Dichotomy Theorem for Constraints on a Three-Element Set
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Constraint solving via fractional edge covers
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Backdoor Sets for DLL Subsolvers
Journal of Automated Reasoning
Perfect Constraints Are Tractable
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Using pivot consistency to decompose and solve functional CSPS
Journal of Artificial Intelligence Research
Backdoors to typical case complexity
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
An efficient arc consistency algorithm for a class of CSP problems
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
Generalizing constraint satisfaction on trees: Hybrid tractability and variable elimination
Artificial Intelligence
Decomposition of domains based on the micro-structure of finite constraint-satisfaction problems
AAAI'93 Proceedings of the eleventh national conference on Artificial intelligence
The structure of tractable constraint satisfaction problems
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Tractable triangles and cross-free convexity in discrete optimisation
Journal of Artificial Intelligence Research
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Much work has been done on describing tractable classes of constraint networks. Most of the known tractable examples are described by either restricting the structure of the networks, or their language. Indeed, for both structural or language restrictions very strong dichotomy results have been proven and in both cases it is likely that all practical examples have already been discovered. As such it is timely to consider tractability which cannot be described by language or structural restrictions. This is the focus of the work here. In this paper we investigate a novel reason for tractability: having at least one variable ordering for which the number of partial solutions to the first n variables is bounded by a polynomial in n. We show that the presence of sufficient functional constraints can guarantee this property and we investigate the complexity of finding good variable orderings based on different notions of functionality. What is more we identify a completely novel reason for tractability based on so called Turan sets.