de.mpg.escidoc.pubman.appbase.FacesBean
English
 
Help Guide Disclaimer Contact us Login
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Report

Improved parallel integer sorting without concurrent writing

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons43989

Albers,  Susanne
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44564

Hagerup,  Torben
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

Locator
There are no locators available
Fulltext (public)

MPI-I-94-137.pdf
(Any fulltext), 17MB

Supplementary Material (public)
There is no public supplementary material available
Citation

Albers, S., & Hagerup, T.(1994). Improved parallel integer sorting without concurrent writing (MPI-I-94-137). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-B799-5
Abstract
We show that $n$ integers in the range $1 \twodots n$ can be stably sorted on an \linebreak EREW PRAM using \nolinebreak $O(t)$ time \linebreak and $O(n(\sqrt{\log n\log\log n}+{{(\log n)^2}/t}))$ operations, for arbitrary given \linebreak $t\ge\log n\log\log n$, and on a CREW PRAM using %$O(\log n\log\log n)$ time and $O(n\sqrt{\log n})$ $O(t)$ time and $O(n(\sqrt{\log n}+{{\log n}/{2^{{t/{\log n}}}}}))$ operations, for arbitrary given $t\ge\log n$. In addition, we are able to sort $n$ arbitrary integers on a randomized CREW PRAM % using %$O(\log n\log\log n)$ time and $O(n\sqrt{\log n})$ operations within the same resource bounds with high probability. In each case our algorithm is a factor of almost $\Theta(\sqrt{\log n})$ closer to optimality than all previous algorithms for the stated problem in the stated model, and our third result matches the operation count of the best known sequential algorithm. We also show that $n$ integers in the range $1 \twodots m$ can be sorted in $O((\log n)^2)$ time with $O(n)$ operations on an EREW PRAM using a nonstandard word length of $O(\log n \log\log n \log m)$ bits, thereby greatly improving the upper bound on the word length necessary to sort integers with a linear time-processor product, even sequentially. Our algorithms were inspired by, and in one case directly use, the fusion trees of Fredman and Willard.