The complexity of (unbounded-arity) Max-CSPs under structural restrictions is poorly understood. The two most general hypergraph properties known to ensure tractability of Max-CSPs, β -acyclicity and bounded (incidence) MIM-width, are incomparable and lead to very different algorithms. We introduce the framework of point decompositions for hypergraphs and use it to derive a new sufficient condition for the tractability of (structurally restricted) Max-CSPs, which generalises both bounded MIM-width and β -acyclicity. On the way, we give a new characterisation of bounded MIM-width and discuss other hypergraph properties which are relevant to the complexity of Max-CSPs, such as β -hypertreewidth.

中文翻译：

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点宽和最大 CSP

在结构限制下（无界）Max-CSP 的复杂性知之甚少。已知的两个最通用的超图属性可确保 Max-CSP 的可处理性，β- 非循环性和有界（发生率）MIM 宽度是无法比较的，并导致非常不同的算法。我们介绍了超图的点分解框架，并使用它来推导出（结构受限的）Max-CSP 的易处理性的新充分条件，它概括了有界 MIM 宽度和β-非周期性。在此过程中，我们给出了有界 MIM 宽度的新特征，并讨论了与 Max-CSP 的复杂性相关的其他超图属性，例如β- 超树宽度。