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  Sorting in linear time?

Andersson, A., Nilsson, S., Hagerup, T., & Raman, R.(1995). Sorting in linear time? (MPI-I-1995-1-024). Saarbrücken: Max-Planck-Institut für Informatik.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0014-A1DE-D Version Permalink: https://hdl.handle.net/11858/00-001M-0000-0019-D47C-4
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 Creators:
Andersson, A.1, Author
Nilsson, S.1, Author
Hagerup, Torben1, Author
Raman, Rajeev1, Author
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, Campus E1 4, 66123 Saarbrücken, DE, ou_24019              

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 Abstract: We show that a unit-cost RAM with a word length of $w$ bits can sort $n$ integers in the range $0\Ttwodots 2^w-1$ in $O(n\log\log n)$ time, for arbitrary $w\ge\log n$, a significant improvement over the bound of $O(n\sqrt{\log n})$ achieved by the fusion trees of Fredman and Willard. Provided that $w\ge(\log n)^{2+\epsilon}$ for some fixed $\epsilon>0$, the sorting can even be accomplished in linear expected time with a randomized algorithm. Both of our algorithms parallelize without loss on a unit-cost PRAM with a word length of $w$ bits. The first one yields an algorithm that uses $O(\log n)$ time and\break $O(n\log\log n)$ operations on a deterministic CRCW PRAM. The second one yields an algorithm that uses $O(\log n)$ expected time and $O(n)$ expected operations on a randomized EREW PRAM, provided that $w\ge(\log n)^{2+\epsilon}$ for some fixed $\epsilon>0$. Our deterministic and randomized sequential and parallel algorithms generalize to the lexicographic sorting problem of sorting multiple-precision integers represented in several words.

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Language(s): eng - English
 Dates: 1995
 Publication Status: Issued
 Pages: 32 p.
 Publishing info: Saarbrücken : Max-Planck-Institut für Informatik
 Table of Contents: -
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 Identifiers: URI: http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1995-1-024
Report Nr.: MPI-I-1995-1-024
BibTex Citekey: AnderssonNilssonHagerupRaman95
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Title: Research Report / Max-Planck-Institut für Informatik
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