Exponential bounds for the running time of a selection algorithm

Hoare's selection algorithm for finding the kth-largest element in a set of n elements is shown to use C comparisons where 1. (i) E( C p ) ⩽ A p n p for some constant A p > 0 and all p ⩾ 1; 2. (ii) P( C n ⩾ u ) ⩽ ( 3 4 ) u(1 + o(1)) as u → ∞. Exact values for the “ A p ” and “ o(1)” terms ar...

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Bibliographic Details
Published inJournal of computer and system sciences Vol. 29; no. 1; pp. 1 - 7
Main Author Devroye, Luc
Format Journal Article
LanguageEnglish
Published Brugge Elsevier Inc 01.01.1984
Academic Press
Subjects
Algorithmics. Computability. Computer arithmetics
Applied sciences
Computer science; control theory; systems
Exact sciences and technology
Theoretical computing
Selection
Probability theory
Algorithm analysis
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ISSN0022-0000
1090-2724
DOI10.1016/0022-0000(84)90009-6

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Summary:Hoare's selection algorithm for finding the kth-largest element in a set of n elements is shown to use C comparisons where 1. (i) E( C p ) ⩽ A p n p for some constant A p > 0 and all p ⩾ 1; 2. (ii) P( C n ⩾ u ) ⩽ ( 3 4 ) u(1 + o(1)) as u → ∞. Exact values for the “ A p ” and “ o(1)” terms are given.
ISSN:0022-0000
1090-2724
DOI:10.1016/0022-0000(84)90009-6