  We provide a smoothed analysis of Hoare's find algorithm and we revisit the
smoothed analysis of quicksort.
  Hoare's find algorithm - often called quickselect - is an easy-to-implement
algorithm for finding the k-th smallest element of a sequence. While the
worst-case number of comparisons that Hoare's find needs is quadratic, the
average-case number is linear. We analyze what happens between these two
extremes by providing a smoothed analysis of the algorithm in terms of two
different perturbation models: additive noise and partial permutations.
  Moreover, we provide lower bounds for the smoothed number of comparisons of
quicksort and Hoare's find for the median-of-three pivot rule, which usually
yields faster algorithms than always selecting the first element: The pivot is
the median of the first, middle, and last element of the sequence. We show that
median-of-three does not yield a significant improvement over the classic rule:
the lower bounds for the classic rule carry over to median-of-three.
