Journal ArticleDOI
Comparisons in Hoare's Find Algorithm
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TLDR
Using trivariate generating functions, an explicit expression is obtained for the variance of the number of comparisons, if the authors search for the jth element in a random permutation of n elements, under the assumption that j is proportional to n.Abstract:
We study the number of comparisons in Hoare's Find algorithm. Using trivariate generating functions, we get an explicit expression for the variance of the number of comparisons, if we search for the jth element in a random permutation of n elements. The variance is also asymptotically evaluated under the assumption that j is proportional to n. Similar results for the number of passes (recursive calls) are given, too.read more
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Journal ArticleDOI
The contraction method for recursive algorithms
Uwe Rösler,Ludger Rüschendorf +1 more
TL;DR: A new quite general model for branching dynamical systems is introduced and the contraction method can be applied in this model and this model includes many classical examples of random trees and gives a general frame for further applications.
Journal ArticleDOI
Optimal Sampling Strategies in Quicksort and Quickselect
Conrado Martínez,Salvador Roura +1 more
TL;DR: The optimal sample size to minimize the average total cost of quicksort, as a function of the size n of the current subarray size, is a, which depends on the selection algorithm and the costs of elementary comparisons and exchanges.
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Quickselect and the Dickman Function
Hsien-Kuei Hwang,Tsung-Hsi Tsai +1 more
TL;DR: In this article, it was shown that the Dickman function is 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 mth-smallest element, where m = o(n).
Quickselect and Dickman function
Hsien-Kuei Hwang,Tsung-Hsi Tsai +1 more
TL;DR: In this article, it was shown that the Dickman function is the limiting distribution of the number of comparisons used by Hoare's quickselect algorithm when given a random permutation of n elements for nding the m-th smallest element, where m = o(n).
Journal ArticleDOI
Cost Decision Support in Product Design
A. Liebers,H.J.J. Kals +1 more
TL;DR: In this paper, a functional architecture for costing data support during product design, as well as a corresponding data structure are presented, which can be used to support cost data support in decision making processes.
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The Art of Computer Programming
TL;DR: The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid.