Approximating the limiting quicksort distribution
James Allen Fill,Svante Janson +1 more
TLDR
This work studies the convergence to the limiting distribution of the sequence of distributions obtained by iterating the transformation S, beginning with a (nearly) arbitrary starting distribution.Abstract:
The limiting distribution of the normalized number of comparisons used by Quicksort to sort an array of n numbers is known to be the unique fixed point with zero mean of a certain distributional transformation S. We study the convergence to the limiting distribution of the sequence of distributions obtained by iterating the transformation S, beginning with a (nearly) arbitrary starting distribution. We demonstrate geometrically fast convergence for various metrics and discuss some implications for numerical calculations of the limiting Quicksort distribution. Finally, we give companion lower bounds which show that the convergence is not faster than geometric. © 2001 John Wiley & Sons, Inc. Random Struct. Alg., 19: 376–406, 2001read more
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Analytic Combinatorics
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Real and Complex Analysis. By W. Rudin. Pp. 412. 84s. 1966. (McGraw-Hill, New York.)
TL;DR: In this paper, the Riesz representation theorem is used to describe the regularity properties of Borel measures and their relation to the Radon-Nikodym theorem of continuous functions.
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Information ranking and power laws on trees
TL;DR: The asymptotic properties of the distribution of R that, in the context of PageRank, represents the frequencies of highly ranked pages are studied and the distributions of R and N are tail equivalent.
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Quicksort asymptotics
James Allen Fill,Svante Janson +1 more
TL;DR: In this article, the first rates of convergence for the distribution of Yn to that of Y, using various metrics, were established for the d2-metric and the rate O(ne - (1/2)) for Kolmogorov-Smirnov distance, for any positive e.g.
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Quicksort asymptotics
James Allen Fill,Svante Janson +1 more
TL;DR: The first rates of convergence for the distribution of Yn to that of Y are provided, using various metrics, and the bound 2n-1/2 in the d2-metric is established and the rate O(ne - ( 1/2)) for Kolmogorov-Smirnov distance is established.
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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.
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An Introduction to Probability Theory and Its Applications.
Book
Real and complex analysis
TL;DR: In this paper, the Riesz representation theorem is used to describe the regularity properties of Borel measures and their relation to the Radon-Nikodym theorem of continuous functions.