Quickselect and the Dickman Function

Authors:
Hsien-Kuei Hwang;Tsung-Hsi Tsai
Affiliations:
Institute of Statistical Science, Academia Sinica, Taipei 115, Taiwan (e-mail: hkhwang@stat.sinica.edu.tw);Institute of Statistical Science, Academia Sinica, Taipei 115, Taiwan (e-mail: hkhwang@stat.sinica.edu.tw)
Venue:
Combinatorics, Probability and Computing
Year:
2002

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Abstract

We show that the limiting distribution of the number of comparisons used by Hoare's quickselect algorithm when given a random permutation of n elements for finding the mth-smallest element, where m = o(n), is the Dickman function. The limiting distribution of the number of exchanges is also derived.