#BIS-Hardness for 2-Spin Systems on Bipartite Bounded Degree Graphs in the Tree Nonuniqueness Region

Jin-Yi Cai; Andreas Galanis; Leslie Ann Goldberg; Heng Guo; Mark Jerrum; Daniel Stefankovic; Eric Vigoda

doi:10.1016/j.jcss.2015.11.009

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arXiv · 1311.4451

#BIS-Hardness for 2-Spin Systems on Bipartite Bounded Degree Graphs in the Tree Nonuniqueness Region

Jin-Yi Cai·Andreas Galanis·Leslie Ann Goldberg·Heng Guo·Mark Jerrum·Daniel Stefankovic·Eric Vigoda

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Abstract

Counting independent sets on bipartite graphs (#BIS) is considered a canonical counting problem of intermediate approximation complexity. It is conjectured that #BIS neither has an FPRAS nor is as hard as #SAT to approximate. We study #BIS in the general framework of two-state spin systems on bipartite graphs. We define two notions, nearly-independent phase-correlated spins and unary symmetry breaking. We prove that it is #BIS-hard to approximate the partition function of any 2-spin system on bipartite graphs supporting these two notions. As a consequence, we classify the complexity of approximating the partition function of antiferromagnetic 2-spin systems on bounded-degree bipartite graphs.

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Jin-Yi Cai, Andreas Galanis, Leslie Ann Goldberg, Heng Guo, Mark Jerrum, Daniel Stefankovic, Eric Vigoda. 2013-11-18. #BIS-Hardness for 2-Spin Systems on Bipartite Bounded Degree Graphs in the Tree Nonuniqueness Region. https://doi.org/10.1016/j.jcss.2015.11.009

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