SIAM Journal on Computing, Volume 49, Issue 4, Page 681-710, January 2020.
We give a fully polynomial-time approximation scheme (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 nonuniqueness 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 $\Delta$.

中文翻译：

---

扩展器图上＃BIS-Hard问题的算法

SIAM计算杂志，第49卷，第4期，第681-710页，2020年1月。
我们为有界二分法中的高烟度硬核模型提供了完整的多项式时间近似方案（FPTAS）和有效的采样算法。扩展度图和有限度扩展图上的低温铁磁Potts模型。结果适用于（例如）随机（二部）$ \ Delta $-正则图，在无限的$ \ Delta $的非唯一性状态下，对于这些问题（伊辛模型除外），没有有效的算法可知-常规树。当$ q $足够小作为$ \ Delta $的函数时，我们还会发现有效的计数和采样算法，用于对随机$ \ Delta $-正则二部图的正确$ q $着色。