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For a graph G, let Z(G,λ) be the partition function of the monomer-dimer system defined by ∑_k m_k(G)λ^k, where m_k(G) is the number of matchings of size k in G. We consider graphs of bounded degree and develop a sublinear-time algorithm for estimating Z(G,λ) at an arbitrary value λ>0 within additive error ϵ n with high probability. The query complexity of our algorithm does not depend on the size of G and is polynomial in 1/ϵ, and we also provide a lower bound quadratic in 1/ϵ for thisarXiv:1208.3629v5 fatcat:5ewl7embvbcn5odnhhbbyaqypq