关于快速排序和Hoare查找的光滑分析
On Smoothed Analysis of Quicksort and Hoare's Find
摘要：
我们提供了一个平滑的霍尔的发现算法的分析，我们重新审视快速排序的平滑分析。霍尔的查找算法-通常称为快速选择-是一个易于实现的算法，用于查找序列的第k个最小元素。虽然霍尔的发现所需的最坏情况下的比较次数是二次的，但平均情况下的比较次数是线性的。我们分析这两个极端之间发生了什么，提供了一个平滑的分析算法在两个不同的扰动模型：加性噪声和部分排列。此外，我们提供了快速排序和霍尔的发现的三个枢轴规则的中位数，这通常会产生更快的算法比总是选择第一个元素的比较平滑的数量的下限：枢轴是中位数的第一个，中间，和序列的最后一个元素。我们表明，中位数的三个不产生显着的改善，经典的规则：下限的经典规则结转到中位数的三个。
英文摘要：
We provide a smoothed analysis of Hoare's find algorithm and we revisit the smoothed analysis of quicksort. Hoare's find algorithm - often called quickselect - is an easy-to-implement algorithm for finding the k-th smallest element of a sequence. While the worst-case number of comparisons that Hoare's find needs is quadratic, the average-case number is linear. We analyze what happens between these two extremes by providing a smoothed analysis of the algorithm in terms of two different perturbation models: additive noise and partial permutations. Moreover, we provide lower bounds for the smoothed number of comparisons of quicksort and Hoare's find for the median-of-three pivot rule, which usually yields faster algorithms than always selecting the first element: The pivot is the median of the first, middle, and last element of the sequence. We show that median-of-three does not yield a significant improvement over the classic rule: the lower bounds for the classic rule carry over to median-of-three.
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