NDLI: Algorithm 489: the algorithm SELECT—for finding the ith smallest of n elements [M1]

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ACM president's letter: about the refereeing process

Matrix reduction—an efficient method

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Expected time bounds for selection

Algorithm 489: the algorithm SELECT—for finding the ith smallest of n elements [M1]

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On computing certain elements of the inverse of a sparse matrix

Discrete least squares polynomial fits

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Algorithm 489: the algorithm SELECT—for finding the ith smallest of n elements [M1]

Content Provider	ACM Digital Library
Author	Rivest, Ronald L. Floyd, Robert W.
Abstract	SELECT will rearrange the values of array segment X[L: R] so that X[K] (for some given K; L ≤ K ≤ R) will contain the (K-L+1)-th smallest value, L ≤ I ≤ K will imply X[I] ≤ X[K], and K ≤ I ≤ R will imply X[I] ≥ X[K. While SELECT is thus functionally equivalent to Hoare's algorithm FIND [1], it is significantly faster on the average due to the effective use of sampling to determine the element T about which to partition X. The average time over 25 trials required by SELECT and FIND to determine the median of n elements was found experimentally to be: n 500 1000 5000 10000 SELECT 89 ms. 141 ms. 493 ms. 877 ms. FIND 104 ms. 197 ms. 1029 ms. 1964 ms. The arbitrary constants 600, .5, and .5 appearing in the algorithm minimize execution time on the particular machine used. SELECT has been shown to run in time asymptotically proportional to N + min (I, N-I), where N = L - R + 1 and I = K - L + 1. A lower bound on the running time within 9 percent of this value has also been proved [2]. Sites [3] has proved SELECT terminates.
File Format	PDF
ISSN	00010782 15577317
DOI	10.1145/360680.360694
Journal	Communications of the ACM (CACM)
Volume Number	18
Issue Number	3
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2005-08-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Medians Quantiles Selection
Content Type	Text
Resource Type	Article
Subject	Computer Science Computer Science

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