max planck institut
informatik

# MPI-I-95-1-024

## Sorting in linear time?

### Andersson, A. and Nilsson, S. and Hagerup, Torben and Raman, Rajeev

MPI-I-95-1-024. September 1995, 32 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
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.
Acknowledgement:
References to related material:

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URL to this document: http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1995-1-024
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