For a graph G on n vertices, let Z(G,λ) be the partition function of the monomer-dimer system defined by: Z(G,λ) = ∑ kmk(G)λ , where mk(G) is the number of matchings of cardinality k in G. We develop a constant-time algorithm for approximating logZ(G,λ) at an arbitrary point λ ≥ 0 with additive error n. In the bounded degree model, the query complexity of… (More)