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On the complexity of H-coloring
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Complexity: knots, colourings and counting
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Complexity of generalized satisfiability counting problems
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On Markov chains for independent sets
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The complexity of counting graph homomorphisms
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Fanout limitations on constraint systems
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Complexity classifications of boolean constraint satisfaction problems
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Theoretical Computer Science
On Counting Independent Sets in Sparse Graphs
SIAM Journal on Computing
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ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
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Proceedings of the forty-first annual ACM symposium on Theory of computing
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SIAM Journal on Computing
An approximation trichotomy for Boolean #CSP
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AAAI'90 Proceedings of the eighth National conference on Artificial intelligence - Volume 1
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On the approximation complexity hierarchy
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
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The degree of a CSP instance is the maximum number of times that any variable appears in the scopes of constraints. We consider the approximate counting problem for Boolean CSP with bounded-degree instances, for constraint languages containing the two unary constant relations {0} and {1}. When the maximum allowed degree is large enough (at least 6) we obtain a complete classification of the complexity of this problem. It is exactly solvable in polynomial time if every relation in the constraint language is affine. It is equivalent to the problem of approximately counting independent sets in bipartite graphs if every relation can be expressed as conjunctions of {0}, {1} and binary implication. Otherwise, there is no FPRAS unless NP=RP. For lower degree bounds, additional cases arise, where the complexity is related to the complexity of approximately counting independent sets in hypergraphs.