  We give an FPTAS for approximating the partition function of the hard-core
model for bipartite graphs when there is sufficient imbalance in the degrees or
fugacities between the sides $(L,R)$ of the bipartition. This includes, among
others, the biregular case when $\lambda=1$ (approximating the number of
independent sets of $G$) and $\Delta_R \geq 7\Delta_L \log(\Delta_L)$. Our
approximation algorithm is based on truncating the cluster expansion of a
polymer model partition function that expresses the hard-core partition
function in terms of deviations from independent sets that are empty on one
side of the bipartition. As a consequence of the method, we also prove that the
hard-core model on such graphs exhibits exponential decay of correlations by
utilizing connections between the cluster expansion and joint cumulants.
