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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| Published in | Journal of computer and system sciences Vol. 29; no. 1; pp. 1 - 7 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Brugge
Elsevier Inc
01.01.1984
Academic Press |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0022-0000 1090-2724 |
| DOI | 10.1016/0022-0000(84)90009-6 |
Cover
| Abstract | 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. |
|---|---|
| AbstractList | 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. |
| Author | Devroye, Luc |
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| Cites_doi | 10.1214/aoms/1177729330 10.1016/S0022-0000(73)80033-9 10.1145/360680.360691 10.1080/01621459.1963.10500830 10.1145/360680.360694 10.1145/366622.366644 10.1016/S0022-0000(76)80029-3 |
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| Keywords | Selection Probability theory Algorithm analysis |
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| References | Floyd, Rivest (BIB6) 1975; 18 Blum, Floyd, Pratt, Rivest, Tarjan (BIB2) 1973; 7 Horowitz, Sahni (BIB9) 1978 Aho, Hopcroft, Ullman (BIB1) 1974 Chernoff (BIB3) 1952; 23 Chow, Teicher (BIB4) 1978 Schonhage, Paterson, Pippenger (BIB11) 1976; 13 Hoeffding (BIB8) 1963; 58 Knuth (BIB10) 1971 Hoare (BIB7) 1961; 4 Floyd, Rivest (BIB5) 1975; 18 Hoeffding (10.1016/0022-0000(84)90009-6_BIB8) 1963; 58 Aho (10.1016/0022-0000(84)90009-6_BIB1) 1974 Hoare (10.1016/0022-0000(84)90009-6_BIB7) 1961; 4 Chow (10.1016/0022-0000(84)90009-6_BIB4) 1978 Floyd (10.1016/0022-0000(84)90009-6_BIB5) 1975; 18 Knuth (10.1016/0022-0000(84)90009-6_BIB10) 1971 Floyd (10.1016/0022-0000(84)90009-6_BIB6) 1975; 18 Blum (10.1016/0022-0000(84)90009-6_BIB2) 1973; 7 Chernoff (10.1016/0022-0000(84)90009-6_BIB3) 1952; 23 Schonhage (10.1016/0022-0000(84)90009-6_BIB11) 1976; 13 Horowitz (10.1016/0022-0000(84)90009-6_BIB9) 1978 |
| References_xml | – volume: 18 start-page: 173 year: 1975 ident: BIB6 article-title: Algorithm 489 publication-title: Comm. ACM – year: 1974 ident: BIB1 article-title: The Design and Analysis of Computer Algorithms – year: 1978 ident: BIB9 article-title: Fundamentals of Computer Algorithms – volume: 13 start-page: 184 year: 1976 end-page: 199 ident: BIB11 article-title: Finding the median publication-title: J. Comput. System Sci. – year: 1978 ident: BIB4 article-title: Probability Theory – volume: 58 start-page: 13 year: 1963 end-page: 30 ident: BIB8 article-title: Probability inequalities for sums of bounded random variables publication-title: J. Amer. Statist. Assoc. – volume: 18 start-page: 165 year: 1975 end-page: 172 ident: BIB5 article-title: Expected time bounds for selection publication-title: Comm. ACM – volume: 4 start-page: 321 year: 1961 end-page: 322 ident: BIB7 article-title: Find (algorithm 65) publication-title: Comm. ACM – year: 1971 ident: BIB10 article-title: Mathematical Analysis of Algorithms publication-title: Computer Science Dept. Report STAN-CS-71-206 – volume: 23 start-page: 493 year: 1952 end-page: 507 ident: BIB3 article-title: A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations publication-title: Ann. Math. Statist. – volume: 7 start-page: 448 year: 1973 end-page: 461 ident: BIB2 article-title: Time bounds for selection publication-title: J. Comput. System Sci. – volume: 23 start-page: 493 year: 1952 ident: 10.1016/0022-0000(84)90009-6_BIB3 article-title: A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations publication-title: Ann. Math. Statist. doi: 10.1214/aoms/1177729330 – year: 1978 ident: 10.1016/0022-0000(84)90009-6_BIB4 – year: 1978 ident: 10.1016/0022-0000(84)90009-6_BIB9 – volume: 7 start-page: 448 year: 1973 ident: 10.1016/0022-0000(84)90009-6_BIB2 article-title: Time bounds for selection publication-title: J. Comput. System Sci. doi: 10.1016/S0022-0000(73)80033-9 – volume: 18 start-page: 165 year: 1975 ident: 10.1016/0022-0000(84)90009-6_BIB5 article-title: Expected time bounds for selection publication-title: Comm. ACM doi: 10.1145/360680.360691 – year: 1974 ident: 10.1016/0022-0000(84)90009-6_BIB1 – volume: 58 start-page: 13 year: 1963 ident: 10.1016/0022-0000(84)90009-6_BIB8 article-title: Probability inequalities for sums of bounded random variables publication-title: J. Amer. Statist. Assoc. doi: 10.1080/01621459.1963.10500830 – volume: 18 start-page: 173 year: 1975 ident: 10.1016/0022-0000(84)90009-6_BIB6 article-title: Algorithm 489 publication-title: Comm. ACM doi: 10.1145/360680.360694 – volume: 4 start-page: 321 year: 1961 ident: 10.1016/0022-0000(84)90009-6_BIB7 article-title: Find (algorithm 65) publication-title: Comm. ACM doi: 10.1145/366622.366644 – year: 1971 ident: 10.1016/0022-0000(84)90009-6_BIB10 article-title: Mathematical Analysis of Algorithms – volume: 13 start-page: 184 year: 1976 ident: 10.1016/0022-0000(84)90009-6_BIB11 article-title: Finding the median publication-title: J. Comput. System Sci. doi: 10.1016/S0022-0000(76)80029-3 |
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| Snippet | 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... |
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| StartPage | 1 |
| SubjectTerms | Algorithmics. Computability. Computer arithmetics Applied sciences Computer science; control theory; systems Exact sciences and technology Theoretical computing |
| Title | Exponential bounds for the running time of a selection algorithm |
| URI | https://dx.doi.org/10.1016/0022-0000(84)90009-6 |
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