快速且完美的子图和聚合系统采样
Fast and perfect sampling of subgraphs and polymer systems
AI总结：
本文提出了一种高效算法，用于根带度图的加权连通诱导子图采样，在亚临界条件下实现完美采样，并应用于聚合模型和非根图let，解决了两种不同问题，改进了自旋系统的采样方法。
摘要：
我们为根带度图的加权连通诱导子图（或图let）提供了一种高效的完美采样算法。该算法利用顶点渗透过程和精心设计的拒绝过滤器，并在渗透亚临界条件下工作。我们证明该条件最优，即当条件不满足时，无限图的（近似）采样在有限期望时间内不可能，有限图的采样则不可行。我们将该采样算法作为子程序，为有限图中的聚合模型和加权非根图let提供近线性时间的完美采样算法，解决两种广泛研究但差异很大的问题。该新的聚合模型完美采样算法为低温度下扩张图和不平衡二分图上的自旋系统提供了改进的采样算法，以及其他应用。
英文摘要：
We give an efficient perfect sampling algorithm for weighted, connected induced subgraphs (or graphlets) of rooted, bounded degree graphs. Our algorithm utilizes a vertex-percolation process with a carefully chosen rejection filter and works under a percolation subcriticality condition. We show that this condition is optimal in the sense that the task of (approximately) sampling weighted rooted graphlets becomes impossible in finite expected time for infinite graphs and intractable for finite graphs when the condition does not hold. We apply our sampling algorithm as a subroutine to give near linear-time perfect sampling algorithms for polymer models and weighted non-rooted graphlets in finite graphs, two widely studied yet very different problems. This new perfect sampling algorithm for polymer models gives improved sampling algorithms for spin systems at low temperatures on expander graphs and unbalanced bipartite graphs, among other applications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
