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DOI: 10.4230/LIPIcs.ICALP.2021.88
URN: urn:nbn:de:0030-drops-141577
URL: https://drops.dagstuhl.de/opus/volltexte/2021/14157/
Koucký, Michal ; Král, Karel
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 |
