We consider the MAP-MRF inference task, that is, minimizing a function of discrete variables represented as a sum of unary and pairwise terms. A prominent approach for tackling this NP-hard problem in practice is to solve its natural LP relaxation and then iteratively tighten the relaxation by adding clusters. Based on some theoretical observations, we propose a new technique for identifying such clusters. It works by running the Singleton Arc Consistency algorithm in a certain CSP instance. Experimental results indicate that the new tightening technique outperforms the previous approach by [Sontag et al. UAI 2012] that searches for frustrated cycles. Our code will be made available at https://github.com/vnk-ist/MAP-MRF/.

翻译：我们考虑MAP-MRF推理任务，即最小化以单变量项和成对项之和表示的离散变量函数。解决这一NP难问题的常用方法是在实践中求解其自然线性规划松弛，然后通过添加聚类迭代收紧松弛。基于一些理论观察，我们提出了一种识别此类聚类的新技术。该技术通过在特定CSP实例中运行Singleton弧一致性算法实现。实验结果表明，新的收紧技术优于[Sontag等人，UAI 2012]中搜索受挫环的先前方法。我们的代码将在https://github.com/vnk-ist/MAP-MRF/ 开源。