2005 | OriginalPaper | Buchkapitel
Towards Optimal Multiple Selection
verfasst von : Kanela Kaligosi, Kurt Mehlhorn, J. Ian Munro, Peter Sanders
Erschienen in: Automata, Languages and Programming
Verlag: Springer Berlin Heidelberg
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The multiple selection problem asks for the elements of rank
r
1
,
r
2
, ...,
r
k
from a linearly ordered set of
n
elements. Let
B
denote the information theoretic lower bound on the number of element comparisons needed for multiple selection. We first show that a variant of multiple quickselect — a well known, simple, and practical generalization of quicksort — solves this problem with
$B+\mathcal{O}(n)$
expected comparisons. We then develop a deterministic divide-and-conquer algorithm that solves the problem in
$\mathcal{O}(B)$
time and
$B+o(B)+\mathcal{O}(n)$
element comparisons.