Time bounds for selection

Manuel Blum; Robert W. Floyd; Vaughan Pratt; Ronald L. Rivest; Robert E. Tarjan

doi:10.1016/S0022-0000(73)80033-9

Time bounds for selection

Manuel Blum, Robert W. Floyd, Vaughan Pratt, Ronald L. Rivest, Robert E. Tarjan

Research output: Contribution to journal › Article › peer-review

886 Scopus citations

Abstract

The number of comparisons required to select the i-th smallest of n numbers is shown to be at most a linear function of n by analysis of a new selection algorithm-PICK. Specifically, no more than 5.4305 n comparisons are ever required. This bound is improved for extreme values of i, and a new lower bound on the requisite number of comparisons is also proved.

Original language	English (US)
Pages (from-to)	448-461
Number of pages	14
Journal	Journal of Computer and System Sciences
Volume	7
Issue number	4
DOIs	https://doi.org/10.1016/S0022-0000(73)80033-9
State	Published - Aug 1973
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science
Applied Mathematics
Computer Networks and Communications
Computational Theory and Mathematics

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10.1016/S0022-0000(73)80033-9

Cite this

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title = "Time bounds for selection",

abstract = "The number of comparisons required to select the i-th smallest of n numbers is shown to be at most a linear function of n by analysis of a new selection algorithm-PICK. Specifically, no more than 5.4305 n comparisons are ever required. This bound is improved for extreme values of i, and a new lower bound on the requisite number of comparisons is also proved.",

author = "Manuel Blum and Floyd, {Robert W.} and Vaughan Pratt and Rivest, {Ronald L.} and Tarjan, {Robert E.}",

note = "Funding Information: work was supported by the National Science Foundation under grant GJ-992.",

year = "1973",

month = aug,

doi = "10.1016/S0022-0000(73)80033-9",

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T1 - Time bounds for selection

AU - Blum, Manuel

AU - Floyd, Robert W.

AU - Pratt, Vaughan

AU - Rivest, Ronald L.

AU - Tarjan, Robert E.

N1 - Funding Information: work was supported by the National Science Foundation under grant GJ-992.

PY - 1973/8

Y1 - 1973/8

N2 - The number of comparisons required to select the i-th smallest of n numbers is shown to be at most a linear function of n by analysis of a new selection algorithm-PICK. Specifically, no more than 5.4305 n comparisons are ever required. This bound is improved for extreme values of i, and a new lower bound on the requisite number of comparisons is also proved.

AB - The number of comparisons required to select the i-th smallest of n numbers is shown to be at most a linear function of n by analysis of a new selection algorithm-PICK. Specifically, no more than 5.4305 n comparisons are ever required. This bound is improved for extreme values of i, and a new lower bound on the requisite number of comparisons is also proved.

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DO - 10.1016/S0022-0000(73)80033-9

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SP - 448

EP - 461

JO - Journal of Computer and System Sciences

JF - Journal of Computer and System Sciences

IS - 4

ER -

Time bounds for selection

Abstract

All Science Journal Classification (ASJC) codes

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