On Probabilistic Networks for Selection, Merging, and Sorting

  title={On Probabilistic Networks for Selection, Merging, and Sorting},
  author={Frank Thomson Leighton and Yuan Ma and Torsten Suel},
  journal={Theory of Computing Systems},
We study comparator networks for selection, merging, and sorting that output the correct result with high probability, given a random input permutation. We prove tight bounds, up to constant factors, on the size and depth of probabilistic (n,k)-selection networks. In the case of (n, n/2)-selection, our result gives a somewhat surprising bound of $\Theta(n \log \log n)$ on the size of networks of success probability in $[\delta, 1-1/\mbox{poly}(n)]$ , where δ is an arbitrarily small positive… CONTINUE READING

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