We give a Markov chain based algorithm for sampling almost uniform solutions of constraint satisfaction problems (CSPs). Assuming a canonical setting for the Lov\'asz local lemma, where each constraint is violated by a small number of forbidden local configurations, our sampling algorithm is accurate in a local lemma regime, and the running time is a fixed polynomial whose dependency on $n$ is close to linear, where $n$ is the number of variables. Our main approach is a new technique called state compression, which generalizes the "mark/unmark" paradigm of Moitra (Moitra, JACM, 2019), and can give fast local-lemma-based sampling algorithms. As concrete applications of our technique, we give the current best almost-uniform samplers for hypergraph colorings and for CNF solutions.

翻译：我们给出了一个基于Markov链的算法,用于取样几乎统一的制约满意度问题解决方案(CSPs )。假设Lov\'asz当地莱马(Lov\'asz当地lemma)的逻辑环境,其中每种制约都受到少量禁止的当地配置的违反,那么我们的取样算法在当地的莱马制度下是准确的,运行时间是一个固定的多元体,其对美元的依赖接近线性,其中对美元的依赖程度接近线性,而美元是变量的数量。我们的主要方法是一种名为“状态压缩”的新技术,它概括了莫伊特拉(Moitra,JACM,2019年)的“标记/非标志”范式,并且可以提供快速的以地方-莱马为基础的取样算法。作为我们技术的具体应用,我们为高光色和CNF溶液提供了目前最佳的几乎统一式取样器。