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arXiv · 1807.04804

Algorithms for #BIS-hard problems on expander graphs

Matthew Jenssen·Peter Keevash·Will Perkins
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Abstract

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 $\Delta$.

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Matthew Jenssen, Peter Keevash, Will Perkins. 2018-07-12. Algorithms for #BIS-hard problems on expander graphs. https://arxiv.org/abs/1807.04804

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