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The Complexity of Approximating Bounded-Degree Boolean #CSP Dyer, Martin Goldberg, Leslie Ann Jalsenius, Markus Richerby, David Boolean constraint satisfaction problem generalized satisfiability counting approximation algorithms The degree of a CSP instance is the maximum number of times that a variable may appear in the scope of constraints. We consider the approximate counting problem for Boolean CSPs with bounded-degree instances, for constraint languages containing the two unary constant relations $\{0\}$ and $\{1\}$. When the maximum degree is at least $25$ 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 $\NPtime = \RPtime$. For lower degree bounds, additional cases arise in which the complexity is related to the complexity of approximately counting independent sets in hypergraphs. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Martin Dyer and Leslie Ann Goldberg and Markus Jalsenius and David Richerby 2010 Is Part Of LIPIcs, Volume 5, 27th International Symposium on Theoretical Aspects of Computer Science (2010) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2010.2466 urn:nbn:de:0030-drops-24669 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2010.2466 eng https://creativecommons.org/licenses/by-nd/3.0/legalcode