A sufficient condition for backtrack-bounded search
Journal of the ACM (JACM)
Tree clustering for constraint networks (research note)
Artificial Intelligence
Finding approximate separators and computing tree width quickly
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Efficient and constructive algorithms for the pathwidth and treewidth of graphs
Journal of Algorithms
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
On the complexity of database queries
Journal of Computer and System Sciences
Conjunctive-query containment and constraint satisfaction
Journal of Computer and System Sciences - Special issue on the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
Fixed-parameter complexity in AI and nonmonotonic reasoning
Artificial Intelligence
Hypertree Decompositions: A Survey
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Constraint solving via fractional edge covers
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
A unified theory of structural tractability for constraint satisfaction and spread cut decomposition
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Hypertree decompositions: structure, algorithms, and applications
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Parameterized Complexity
Local search for optimal global map generation using mid-decadal landsat images
IAAI'08 Proceedings of the 20th national conference on Innovative applications of artificial intelligence - Volume 3
Constraint satisfaction with bounded treewidth revisited
Journal of Computer and System Sciences
Tradeoffs in the complexity of backdoor detection
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Algorithms for propositional model counting
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Learning cluster-based structure to solve constraint satisfaction problems
Annals of Mathematics and Artificial Intelligence
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The constraint satisfaction problem can be solved in polynomial time for instances where certain parameters (e.g., the treewidth of primal graphs) are bounded. However, there is a trade-off between generality and performance: larger bounds on the parameters yield worse time complexities. It is desirable to pay for more generality only by a constant factor in the running time, not by a larger degree of the polynomial. Algorithms with such a uniform polynomial time complexity are known as fixed-parameter algorithms. In this paper we determine whether or not fixed-parameter algorithms for constraint satisfaction exist, considering all possible combinations of the following parameters: the treewidth of primal graphs, the treewidth of dual graphs, the treewidth of incidence graphs, the domain size, the maximum arity of constraints, and the maximum size of overlaps of constraint scopes. The negative cases are subject to the complexity theoretic assumption FPT ≠ W[1] which is the parameterized analog to P ≠ NP. For the positive cases we provide an effective fixed-parameter algorithm which is based on dynamic programming on “nice” tree decompositions.