Algorithms for #BIS-hard problems on expander graphs

Matthew Jenssen, Will Perkins, Peter Keevash

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We give an FPTAS and an efficient sampling algorithm for the high-fugacity hard-core model on bounded-degree bipartite expander graphs and the low-temperature ferromagnetic Potts model on bounded-degree expander graphs. The results apply, for example, to random (bipartite) $\Delta$-regular graphs, for which no efficient algorithms were known for these problems (with the exception of the Ising model) in the non-uniqueness regime of the infinite $\Delta$-regular tree. We also find efficient counting and sampling algorithms for proper $q$-colorings of random $\Delta$-regular bipartite graphs when $q$ is sufficiently small as a function of $\Delta$.
Original languageEnglish
JournalSIAM Journal on Computing
Publication statusAccepted/In press - 28 May 2020


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