# 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

**BibTeX**
`@TECHREPORT{``AnderssonNilssonHagerupRaman95``,`

` AUTHOR = {Andersson, A. and Nilsson, S. and Hagerup, Torben and Raman, Rajeev},`

` TITLE = {Sorting in linear time?},`

` TYPE = {Research Report},`

` INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},`

` ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},`

` NUMBER = {MPI-I-95-1-024},`

` MONTH = {September},`

` YEAR = {1995},`

` ISSN = {0946-011X},`

`}`