@techreport{Rub97,
TITLE = {On Batcher's Merge Sorts as Parallel Sorting Algorithms},
AUTHOR = {R{\"u}b, Christine},
LANGUAGE = {eng},
NUMBER = {MPI-I-1997-1-012},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
ADDRESS = {Saarbr{\"u}cken},
YEAR = {1997},
DATE = {1997},
ABSTRACT = {In this paper we examine the average running times of Batcher's bitonic<br>merge and Batcher's odd-even merge when they are used as parallel merging<br>algorithms. It has been shown previously that the running time of<br>odd-even merge can be upper bounded by a function of the maximal rank difference<br>for elements in the two input sequences. Here we give an almost matching lower bound<br>for odd-even merge as well as a similar upper bound for (a special version<br>of) bitonic merge.<br>>From this follows that the average running time of odd-even merge (bitonic<br>merge) is $\Theta((n/p)(1+\log(1+p^2/n)))$ ($O((n/p)(1+\log(1+p^2/n)))$, resp.)<br>where $n$ is the size of the input and $p$ is the number of processors used. <br>Using these results we then show that the average running times of<br>odd-even merge sort and bitonic merge sort are $O((n/p)(\log n + (\log(1+p^2/n))^2))$,<br>that is, the two algorithms are optimal on the average if <br>$n\geq p^2/2^{\sqrt{\log p}}$.<br>The derived bounds do not allow to compare the two sorting algorithms<br>program, for various sizes of input and numbers of processors.<br>},
TYPE = {Research Report / Max-Planck-Institut für Informatik},
}