License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.AofA.2020.22
URN: urn:nbn:de:0030-drops-120529
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12052/
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Neininger, Ralph ; Straub, Jasmin

Convergence Rates in the Probabilistic Analysis of Algorithms

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LIPIcs-AofA-2020-22.pdf (0.4 MB)

Abstract

In this extended abstract a general framework is developed to bound rates of convergence for sequences of random variables as they mainly arise in the analysis of random trees and divide-and-conquer algorithms. The rates of convergence are bounded in the Zolotarev distances. Concrete examples from the analysis of algorithms and data structures are discussed as well as a few examples from other areas. They lead to convergence rates of polynomial and logarithmic order. Our results show how to obtain a significantly better bound for the rate of convergence when the limiting distribution is Gaussian.

BibTeX - Entry

@InProceedings{neininger_et_al:LIPIcs:2020:12052,
  author =	{Ralph Neininger and Jasmin Straub},
  title =	{{Convergence Rates in the Probabilistic Analysis of Algorithms}},
  booktitle =	{31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020)},
  pages =	{22:1--22:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-147-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{159},
  editor =	{Michael Drmota and Clemens Heuberger},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12052},
  URN =		{urn:nbn:de:0030-drops-120529},
  doi =		{10.4230/LIPIcs.AofA.2020.22},
  annote =	{Keywords: weak convergence, probabilistic analysis of algorithms, random trees, probability metrics}
}

Keywords: weak convergence, probabilistic analysis of algorithms, random trees, probability metrics
Collection: 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020)
Issue Date: 2020
Date of publication: 10.06.2020

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