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要旨:
This paper is concerned with the average running time of Batcher's
odd-even merge sort when implemented on a collection of processors.
We consider the case where $n$, the size of the input,
is an arbitrary multiple of the number $p$ of processors used.
We show that Batcher's odd-even merge (for two sorted lists of length $n$ each)
can be implemented to run in time $O((n/p)(\log (2+p^2/n)))$ on the average,
and that odd-even merge sort can be implemented to run in time
$O((n/p)(\log n+\log p\log (2+p^2/n)))$ on the average.
In the case of merging (sorting), the average is taken over all possible outcomes
of the merging (all possible permutations of $n$ elements).
That means that odd-even merge and odd-even merge sort have an optimal
average running time if $n\geq p^2$. The constants involved are also
quite small.
