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On Batcher's Merge Sorts as Parallel Sorting Algorithms

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons45318

Rüb,  Christine
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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1997-1-012
(Any fulltext), 11KB

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Citation

Rüb, C.(1997). On Batcher's Merge Sorts as Parallel Sorting Algorithms (MPI-I-1997-1-012). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-9E16-4
Abstract
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.