License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2021.88
URN: urn:nbn:de:0030-drops-141577
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14157/
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Koucký, Michal ; Král, Karel

Sorting Short Integers

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LIPIcs-ICALP-2021-88.pdf (0.7 MB)

Abstract

We build boolean circuits of size ?(nm²) and depth ?(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 ?(nmk (1 + log^*(n) - log^*(m))) and depth ?(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
Collection: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Issue Date: 2021
Date of publication: 02.07.2021

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