Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Koucký, Michal; Král, Karel https://www.dagstuhl.de/lipics License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-141577
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Sorting Short Integers

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Abstract

We build boolean circuits of size 𝒪(nm²) and depth 𝒪(log(n) + m log(m)) for sorting n integers each of m-bits. We build also circuits that sort n integers each of m-bits according to their first k bits that are of size 𝒪(nmk (1 + log^*(n) - log^*(m))) and depth 𝒪(log³(n)). This improves on the results of Asharov et al. [Asharov et al., 2021] and resolves some of their open questions.

BibTeX - Entry

@InProceedings{koucky_et_al:LIPIcs.ICALP.2021.88,
  author =	{Kouck\'{y}, Michal and Kr\'{a}l, Karel},
  title =	{{Sorting Short Integers}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{88:1--88:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14157},
  URN =		{urn:nbn:de:0030-drops-141577},
  doi =		{10.4230/LIPIcs.ICALP.2021.88},
  annote =	{Keywords: sorting, small integers, boolean circuits}
}

Keywords: sorting, small integers, boolean circuits
Seminar: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Issue date: 2021
Date of publication: 02.07.2021


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