线性规划和凸包变得很容易

SCG '90 Pub Date : 1990-05-01 DOI:10.1145/98524.98570

R. Seidel

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引用次数: 206

摘要

我们提出了两种随机算法。一种是在期望时间(m)内解决涉及d个变量的m个约束的线性规划。另一种是在期望时间&Ogr;(n≤d/2)内构造Rd中n个点的凸包，d > 3。在两个界内，d都被认为是常数。在线性规划算法中，时间边界对d的依赖形式为d!我们的结果的主要优点在于算法及其分析的绝对简单。

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Linear programming and convex hulls made easy

We present two randomized algorithms. One solves linear programs involving m constraints in d variables in expected time &Ogr;(m). The other constructs convex hulls of n points in Rd, d > 3, in expected time &Ogr;(n⌈d/2⌉). In both bounds d is considered to be a constant. In the linear programming algorithm the dependence of the time bound on d is of the form d!. The main virtue of our results lies in the utter simplicity of the algorithms as well as their analyses.

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来源期刊

SCG '90

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