工业SAT集群中的群落结构
Community Structure in Industrial SAT Instances
摘要：
现代SAT求解器在解决工业实例方面取得了显着进展。大多数技术都是经过密集的实验过程开发出来的。据信，这些技术利用了工业实例的底层结构。然而，很少有作品试图准确地描述这种结构的主要特征。复杂网络研究界已经开发出分析技术和算法来研究可供SAT社区使用的真实世界图。最近，已经有一些尝试来分析复杂网络方面的工业SAT实例的结构，目的是解释SAT解决技术的成功，并可能改进它们。在本文中，复杂网络的结果的启发，我们研究的社区结构，或模块化，工业SAT实例。在一个具有清晰社区结构或高模块化的图中，我们可以找到一个将其节点划分为社区的分区，使得大多数边连接同一社区的变量。在我们的分析中，我们表示SAT实例的图形，我们表明，大多数应用程序的基准测试的特点是高模块化。相反，随机SAT实例更接近经典的Erdös-Rényi随机图模型，其中没有结构可以观察到。我们还分析了这种结构如何演变的CDCL SAT求解器的执行的影响。特别是，我们使用社区结构来检测求解器在搜索过程中学习到的新子句有助于破坏公式的原始结构。也就是说，习得性从句倾向于包含不同社区的变量。
英文摘要：
Modern SAT solvers have experienced a remarkable progress on solving industrial instances. Most of the techniques have been developed after an intensive experimental process. It is believed that these techniques exploit the underlying structure of industrial instances. However, there are few works trying to exactly characterize the main features of this structure. The research community on complex networks has developed techniques of analysis and algorithms to study real-world graphs that can be used by the SAT community. Recently, there have been some attempts to analyze the structure of industrial SAT instances in terms of complex networks, with the aim of explaining the success of SAT solving techniques, and possibly improving them. In this paper, inspired by the results on complex networks, we study the community structure, or modularity, of industrial SAT instances. In a graph with clear community structure, or high modularity, we can find a partition of its nodes into communities such that most edges connect variables of the same community. In our analysis, we represent SAT instances as graphs, and we show that most application benchmarks are characterized by a high modularity. On the contrary, random SAT instances are closer to the classical Erdös-Rényi random graph model, where no structure can be observed. We also analyze how this structure evolves by the effects of the execution of a CDCL SAT solver. In particular, we use the community structure to detect that new clauses learned by the solver during the search contribute to destroy the original structure of the formula. This is, learned clauses tend to contain variables of distinct communities.
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