Numerous fundamental database and reasoning problems are known to be NP-hard in general but tractable on instances where the underlying hypergraph structure is $\beta$-acyclic. Despite the importance of many of these problems, there has been little success in generalizing these results beyond acyclicity. In this paper, we take on this challenge and propose nest-set width, a novel generalization of hypergraph $\beta$-acyclicity. We demonstrate that nest-set width has desirable properties and algorithmic significance. In particular, evaluation of boolean conjunctive queries with negation is tractable for classes with bounded nest-set width. Furthermore, propositional satisfiability is fixed-parameter tractable when parameterized by nest-set width.
翻译:众所周知,许多基本数据库和推理问题一般都是NP硬的,但在一些情况下,基本的高压结构是 $\ beta$- ancyclical 。尽管其中许多问题都很重要,但除了周期性之外,在推广这些结果方面没有取得多少成功。在本文中,我们迎接这一挑战并提出巢状宽度,这是对高压 $\ beta$- ancyclicity的新的概括。我们证明,巢状宽度具有可取的特性和算法意义。特别是,对与否定相连接的布尔恩相连接的查询的评价对于有捆绑的巢状宽度的班类来说是可行的。此外,在按巢状宽度进行参数比较时,假设的参数参数是固定的。