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DOI: 10.4230/LIPIcs.AofA.2018.21

On the Tails of the Limiting QuickSort Density

Authors: James Allen Fill and Wei-Chun Hung

Published in: LIPIcs, Volume 110, 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)

Abstract

We give upper and lower asymptotic bounds for the left tail and for the right tail of the continuous limiting QuickSort density f that are nearly matching in each tail. The bounds strengthen results from a paper of Svante Janson (2015) concerning the corresponding distribution function F. Furthermore, we obtain similar upper bounds on absolute values of derivatives of f of each order.

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James Allen Fill and Wei-Chun Hung. On the Tails of the Limiting QuickSort Density. In 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 110, pp. 21:1-21:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{fill_et_al:LIPIcs.AofA.2018.21,
  author =	{Fill, James Allen and Hung, Wei-Chun},
  title =	{{On the Tails of the Limiting QuickSort Density}},
  booktitle =	{29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)},
  pages =	{21:1--21:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-078-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{110},
  editor =	{Fill, James Allen and Ward, Mark Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2018.21},
  URN =		{urn:nbn:de:0030-drops-89144},
  doi =		{10.4230/LIPIcs.AofA.2018.21},
  annote =	{Keywords: Quicksort, density tails, asymptotic bounds, Landau-Kolmogorov inequality}
}

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On the Tails of the Limiting QuickSort Density

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