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Sorting Short Integers

Authors Michal Koucký , Karel Král

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Subject Classification

ACM Subject Classification
  • Theory of computation → Sorting and searching
Keywords
  • sorting
  • small integers
  • boolean circuits

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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.

Cite As Get BibTex

Michal Koucký and Karel Král. Sorting Short Integers. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 88:1-88:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ICALP.2021.88

Author Details

Michal Koucký
  • Computer Science Institute, Charles University, Prague, Czech Republic
Karel Král
  • Computer Science Institute, Charles University, Prague, Czech Republic

Funding

Michal Koucký and Karel Král were supported by the Grant Agency of the Czech Republic under the grant agreement no. 19-27871X. Karel Král was also partially supported by the Charles University project SVV–2020–260578.

Acknowledgements

The authors are grateful for insightful discussions with Mike Saks on sorting and to Veronika Slívová for her insights and comments regarding the first versions of this paper. The authors thank Igor Sergeev for pointing us to the paper of Kospanov [Kospanov, 1994].

References

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