We give an efficient perfect sampling algorithm for weighted, connected induced subgraphs (or graphlets) of rooted, bounded degree graphs under a vertex-percolation subcriticality condition. We show that this subcriticality condition is optimal in the sense that the problem of (approximately) sampling weighted rooted graphlets becomes impossible for infinite graphs and intractable for finite graphs if the condition does not hold. We apply our rooted graphlet sampling algorithm as a subroutine to give a fast perfect sampling algorithm for polymer models and a fast perfect sampling algorithm for weighted non-rooted graphlets in finite graphs, two widely studied yet very different problems. We apply this polymer model algorithm to give improved sampling algorithms for spin systems at low temperatures on expander graphs and other structured families of graphs: under the least restrictive conditions known we give near linear-time algorithms, while previous algorithms in these regimes required large polynomial running times.

翻译：我们给出一个高效的完美抽样算法,用于根基、连接引导的底部、底部、底部、底部、底部、底部的子图(或石墨),以备在顶部、底部次临界状态条件下使用。我们显示,这个亚临界状态状态最理想,因为(大约)抽样加权根部石墨的问题对于无限图来说是不可能的,如果条件不维持,对于定数图来说也难以解决。我们用我们根基的石墨取样算法作为子例,为聚合物模型提供一个快速完美的取样算法,为加权、非底部、定点、两个广泛研究但非常不同的问题提供一个快速完美的取样算法。我们应用这个聚合物模型算法,在扩张式图和其他结构化的图表组别上,为低温的旋转系统提供更好的取样算法:在已知的最小限制性条件下,我们提供了近线性算法,而这些系统中以前的算法则需要大型多数值运行时间。