The 0/1 knapsack polytope is the convex hull of all 0/1 vectors that satisfy a given single linear inequality with non-negative coefficients. This paper provides a comprehensive overview of knapsack polytopes. We discuss basic polyhedral properties, (lifted) cover and other valid inequalities, cases for which complete linear descriptions are known, geometric properties for small dimensions, and connections to independence systems. We also discuss the generalization to (mixed-)integer knapsack polytopes and variants.

中文翻译：

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背包多胞体：一项调查

0/1 背包多面体是所有 0/1 向量的凸包，这些向量满足具有非负系数的给定单个线性不等式。本文提供了背包多胞体的全面概述。我们讨论基本的多面体属性、（提升的）覆盖和其他有效的不等式、已知完整线性描述的情况、小维度的几何属性以及与独立系统的连接。我们还讨论了对（混合）整数背包多面体和变体的推广。