Abstract
By implementing algorithmic versions of Sapozhenko's graph container methods, we give new algorithms for approximating the number of independent sets in bipartite graphs. The first algorithm applies to d-regular, bipartite graphs satisfying a weak expansion condition: when d is constant, and the graph is a Ω(log2 d/d)-bipartite expander, we obtain an FPTAS for the number of independent sets. Previously such a result for d > 5 was known only for graphs satisfying the much stronger expansion conditions of random graphs. The second algorithm applies to all d-regular, bipartite graphs, runs in time exp , and outputs a (1 + o(1))-approximation to the number of independent sets.
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