In this paper we present a scaling algorithm for minimizing arbitrary functions over vertices of polytopes in an oracle model of computation which includes an augmentation oracle. For the binary case, when the vertices are 0–1 vectors, we show that the oracle time is polynomial. Also, this algorithm allows us to generalize some concepts of combinatorial optimization concerning performance bounds of greedy algorithms and leads to new bounds for the complexity of the simplex method.

中文翻译：

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一种优化多面体顶点上任意函数的缩放算法

在本文中，我们提出了一种缩放算法，用于在包括增强预言机的预言机计算模型中最小化多胞体顶点上的任意函数。对于二元情况，当顶点是 0-1 向量时，我们证明预言时间是多项式的。此外，该算法允许我们概括一些关于贪婪算法性能界限的组合优化概念，并为单纯形方法的复杂性带来新的界限。