Abstract
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 the size n 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 m each) can be implemented to run in time O((m/p)(1+log(1+p 2/m))) on the average, and that odd-even merge sort can be implemented to run in time O((n/p)(log(n/p)+logp(1+log(1+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≥p 2.
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© 1995 Springer-Verlag Berlin Heidelberg
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Rüb, C. (1995). On the average running time of odd-even merge sort. In: Mayr, E.W., Puech, C. (eds) STACS 95. STACS 1995. Lecture Notes in Computer Science, vol 900. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59042-0_99
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DOI: https://doi.org/10.1007/3-540-59042-0_99
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