QUICKSELECT Revisited
نویسنده
چکیده مقاله:
We give an overview of the running time analysis of the random divide-and-conquer algorithm FIND or QUICKSELECT. The results concern moments, distribution of FIND’s running time, the limiting distribution, a stochastic bound and the key: a stochastic fixed point equation.
منابع مشابه
On Quickselect, partial sorting and Multiple Quickselect
We present explicit solutions of a class of recurrences related to the Quickselect algorithm. Thus we are immediately able to solve recurrences arising at the partial sorting problem, which are contained in this class. We show how the partial sorting problem is connected to the Multiple Quickselect algorithm and present a method for the calculation of solutions for a class of recurrences relate...
متن کاملRandomized Algorithms: QuickSort and QuickSelect
Let Q(A) be number of comparisons done on input array A: (A) For 1 ≤ i < j < n let R ij be the event that rank i element is compared with rank j element. (B) X ij is the indicator random variable for R ij. That is, X ij = 1 if rank i is compared with rank j element, otherwise 0. Q(A) = ∑ 1≤i<j≤n X ij and hence by linearity of expectation,
متن کاملQuickselect and Dickman function
We show that the limiting distribution of the number of comparisons used by Hoare’s quickselect algorithm when given a random permutation of n elements for finding the m-th smallest element, where m = o(n), is the Dickman function. The limiting distribution of the number of exchanges is also derived. 1 Quickselect Quickselect is one of the simplest and efficient algorithms in practice for findi...
متن کاملQuickSelect: history-based selection expansion
When editing a graphical document, it is common to apply a change to multiple items at once, and a variety of tools exist for selecting sets of items. However, directly selecting large sets can sometimes be cumbersome and repetitive. We propose a method for helping users reuse complex selections by expanding the set of currently selected items. We analyze a document’s operation history to deter...
متن کاملRandomized Algorithms: QuickSort and QuickSelect
(A) Let Q(A) be number of comparisons done on input array A: (A) R ij : event that rank i element is compared with rank j element, for 1 ≤ i < j ≤ n. (B) X ij is the indicator random variable for R ij. That is, X ij = 1 if rank i is compared with rank j element, otherwise 0. (B) Q(A) = ∑ 1≤i<j≤n X ij. (C) By linearity of expectation,
متن کاملOn the Variance of Quickselect
Quickselect with median-of-three is routinely used as the method of choice for selection of the mth element out of n in general-purpose libraries such as the C++ Standard Template Library. Its average behavior is fairly well understood and has been shown to outperform that of the standard variant, which chooses a random pivot on each stage. However, no results were previously known about the va...
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عنوان ژورنال
دوره 3 شماره None
صفحات 271- 296
تاریخ انتشار 2004-11
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