Abstract
Comparator networks of constant depth can be used for sorting in the following way. The computation consists of a number of iterations, say t, each iteration being a single run through the comparator network. The output of iteration j (j < t) is used as the input for iteration j+1. The output of the iteration t is the output of the computation. In such a way, it is possible to apply a network with a small number of comparators for sorting long input sequences. However, it is not clear how to make such a computation fast.
Odd-Even Transposition Sort gives a periodic sorting network of depth 2, that sorts n numbers in n/2 iterations. The network of depth 8 proposed by Schwiegelshohn [8] sorts n numbers in O(√nlog n) iterations. Krammer
For a fixed but arbitrary k ∃ ℕ, we present a periodic sorting network of depth O(k) that sorts n input numbers in O(k2 · n1/k) steps.
supported by KBN grant 2 1197 91 01 and Volkswagen Foundation, Project “Paralleles Rechnen: Theoretische und experimentelle Untersuchungen zu parallelen Rechnenmodellen und systemnahen Algorithmen”, partially this work was done while the first and the second author visited Heinz-Nixdorf-Institut, Universität Paderborn
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© 1994 Springer-Verlag Berlin Heidelberg
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Kik, M., Kutyłowski, M., Stachowiak, G. (1994). Periodic constant depth sorting networks. In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds) STACS 94. STACS 1994. Lecture Notes in Computer Science, vol 775. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57785-8_142
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DOI: https://doi.org/10.1007/3-540-57785-8_142
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