MPI-INF/SWS Research Reports 1991-2021

# MPI-I-97-1-012

## On Batcher's Merge Sorts as Parallel Sorting Algorithms

### Rüb, Christine

#### June 1997, 23 pages.

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##### Status: available - back from printing

In this paper we examine the average running times of Batcher's bitonic merge and Batcher's odd-even merge when they are used as parallel merging algorithms. It has been shown previously that the running time of odd-even merge can be upper bounded by a function of the maximal rank difference for elements in the two input sequences. Here we give an almost matching lower bound for odd-even merge as well as a similar upper bound for (a special version of) bitonic merge. >From this follows that the average running time of odd-even merge (bitonic merge) is $\Theta((n/p)(1+\log(1+p^2/n)))$ ($O((n/p)(1+\log(1+p^2/n)))$, resp.) where $n$ is the size of the input and $p$ is the number of processors used. Using these results we then show that the average running times of odd-even merge sort and bitonic merge sort are $O((n/p)(\log n + (\log(1+p^2/n))^2))$, that is, the two algorithms are optimal on the average if $n\geq p^2/2^{\sqrt{\log p}}$. The derived bounds do not allow to compare the two sorting algorithms program, for various sizes of input and numbers of processors.

• Attachement: MPI-I-97-1-012.ps (246 KBytes)

URL to this document: https://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1997-1-012

BibTeX
@TECHREPORT{Rüb97,
AUTHOR = {R{\"u}b, Christine},
TITLE = {On Batcher's Merge Sorts as Parallel Sorting Algorithms},
TYPE = {Research Report},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
NUMBER = {MPI-I-97-1-012},
MONTH = {June},
YEAR = {1997},
ISSN = {0946-011X},
}