Abstract
This paper provides an analysis of a natural d-round tournament over n = 2d players and demonstrates that the tournament possesses a surprisingly strong ranking property. The ranking property of this tournament is used to design efficient sorting algorithms for several models of parallel computation: a comparator network of depth $c\\cdot\lg n$, $c\approx 7.44$, that sorts the vast majority of the n! possible input permutations; an $O(\lg n)$-depth hypercubic comparator network that sorts the vast majority of permutations; a hypercubic sorting network with nearly logarithmic depth; an $O(\lg n)$-time randomized sorting algorithm for any hypercubic machine (other such algorithms have been previously discovered, but this algorithm has a significantly smaller failure probability than any previously known algorithm); and a randomized algorithm for sorting nO (m)-bit records on an $(n\lg n)$-node omega machine in $O(m+\lg n)$ bit steps.
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