License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.SoCG.2020.29
URN: urn:nbn:de:0030-drops-121873
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12187/
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Cheng, Siu-Wing ; Chiu, Man-Kwun ; Jin, Kai ; Wong, Man Ting

A Generalization of Self-Improving Algorithms

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LIPIcs-SoCG-2020-29.pdf (0.5 MB)

Abstract

Ailon et al. [SICOMP'11] proposed self-improving algorithms for sorting and Delaunay triangulation (DT) when the input instances x₁,⋯,x_n follow some unknown product distribution. That is, x_i comes from a fixed unknown distribution ?_i, and the x_i’s are drawn independently. After spending O(n^{1+ε}) time in a learning phase, the subsequent expected running time is O((n+ H)/ε), where H ∈ {H_S,H_DT}, and H_S and H_DT are the entropies of the distributions of the sorting and DT output, respectively. In this paper, we allow dependence among the x_i’s under the group product distribution. There is a hidden partition of [1,n] into groups; the x_i’s in the k-th group are fixed unknown functions of the same hidden variable u_k; and the u_k’s are drawn from an unknown product distribution. We describe self-improving algorithms for sorting and DT under this model when the functions that map u_k to x_i’s are well-behaved. After an O(poly(n))-time training phase, we achieve O(n + H_S) and O(nα(n) + H_DT) expected running times for sorting and DT, respectively, where α(⋅) is the inverse Ackermann function.

BibTeX - Entry

@InProceedings{cheng_et_al:LIPIcs:2020:12187,
  author =	{Siu-Wing Cheng and Man-Kwun Chiu and Kai Jin and Man Ting Wong},
  title =	{{A Generalization of Self-Improving Algorithms}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{29:1--29:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Sergio Cabello and Danny Z. Chen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12187},
  URN =		{urn:nbn:de:0030-drops-121873},
  doi =		{10.4230/LIPIcs.SoCG.2020.29},
  annote =	{Keywords: expected running time, entropy, sorting, Delaunay triangulation}
}

Keywords: expected running time, entropy, sorting, Delaunay triangulation
Collection: 36th International Symposium on Computational Geometry (SoCG 2020)
Issue Date: 2020
Date of publication: 08.06.2020

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