The problem of uniformly sampling hypergraph independent sets is revisited. We design an efficient perfect sampler for the problem under a condition similar to that of the asymmetric Lov\'asz Local Lemma. When applied to $d$-regular $k$-uniform hypergraphs on $n$ vertices, our sampler terminates in expected $O(n\log n)$ time provided $d\le c\cdot 2^{k/2}/k$ for some constant $c>0$. If in addition the hypergraph is linear, the condition can be weaken to $d\le c\cdot 2^{k}/k^2$ for some constant $c>0$, matching the rapid mixing condition for Glauber dynamics in Hermon, Sly and Zhang [HSZ19].
翻译：统一采样高频独立集体的问题被重新讨论。 我们设计了一个高效完美的问题取样器, 其条件与不对称的Lov\'asz本地 Lemma类似。 当应用到美元正值美元对美元脊椎的美元正值美元单体高光谱时, 我们的采样器以预期的美元( n\log n) 时间终止 $O (n\log n) 提供 $d\le c\ c\ cdot 2\ k/2}/k$, 以某种恒定的 Hermon, Sly 和Zhang [HSZ19] 的Grauber 动态快速混合状态。 如果高光谱是线性, 条件可能会被削弱至$d\le c\ cdot 2\ k}k}/k ⁇ 2$2$, 与恒定值 $c>0美元相匹配 。
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