On tree width, bramble size, and expansion
Journal of Combinatorial Theory Series B
Universal augmentation schemes for network navigability
Theoretical Computer Science
A note on width-parameterized SAT: An exact machine-model characterization
Information Processing Letters
Approximating fractional hypertree width
ACM Transactions on Algorithms (TALG)
On the complexity of circuit satisfiability
Proceedings of the forty-second ACM symposium on Theory of computing
Tractable hypergraph properties for constraint satisfaction and conjunctive queries
Proceedings of the forty-second ACM symposium on Theory of computing
The Necessity of Bounded Treewidth for Efficient Inference in Bayesian Networks
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Algorithmic lower bounds for problems parameterized by clique-width
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Does treewidth help in modal satisfiability?
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Known algorithms on graphs of bounded treewidth are probably optimal
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
On moderately exponential time for SAT
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
Constraint satisfaction problems: convexity makes all different constraints tractable
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
On the algorithmic effectiveness of digraph decompositions and complexity measures
Discrete Optimization
Constraint satisfaction problems: Convexity makes AllDifferent constraints tractable
Theoretical Computer Science
Does Treewidth Help in Modal Satisfiability?
ACM Transactions on Computational Logic (TOCL)
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It is well-known that constraint satisfaction problems (CSP) can be solved in time n^{{\rm O}(k)} if the treewidth of the primal graph of the instance is at most k and n is the size of the input. We show that no algorithm can be significantly better than this treewidth-based algorithm, even if we restrict the problem to some special class of primal graphs. Formally, let G be an arbitrary class of graphs and assume that there is an algorithm A solving binary CSP for instances whose primal graph is in G . We prove that if the running time of A is f(G)n^{{\rm O}(k/\log k)}, where k is the treewidth of the primal graph G and f is an arbitrary function, then the Exponential Time Hypothesis fails. We prove the result also in the more general framework of the homomorphism problem for bounded-arity relational structures. For this problem, the treewidth of the core of the left-hand side structure plays the same role as the treewidth of the primal graph above.