One classical sorting algorithm, whose performance in many cases remains unanalyzed, is Shellsort. Let h be a t-component vector of positive integers. An h-Shellsort will sort any given n elements in t passes, by means of comparisons and exchanges of elements. Let S>j(h; n) denote the average number of element exchanges in the jth pass, assuming that all the n! initial orderings are equally likely. In this paper we derive asymptotic formulas of Sj(h; n) for any fixed h = (h, k, l), making use of a new combinatorial interpretation of S3. For the special case h = (3, 2, 1), the analysis is further sharpened to yield exact expressions.
%0 Journal Article
%1 yao80
%A Yao, Andrew Chi-Chih
%D 1980
%J Journal of Algorithms
%K algorithm shellsort sorting
%N 1
%P 14--50
%R 10.1016/0196-6774(80)90003-6
%T An Analysis of $(h, k, 1)$-Shellsort
%V 1
%X One classical sorting algorithm, whose performance in many cases remains unanalyzed, is Shellsort. Let h be a t-component vector of positive integers. An h-Shellsort will sort any given n elements in t passes, by means of comparisons and exchanges of elements. Let S>j(h; n) denote the average number of element exchanges in the jth pass, assuming that all the n! initial orderings are equally likely. In this paper we derive asymptotic formulas of Sj(h; n) for any fixed h = (h, k, l), making use of a new combinatorial interpretation of S3. For the special case h = (3, 2, 1), the analysis is further sharpened to yield exact expressions.
@article{yao80,
abstract = {One classical sorting algorithm, whose performance in many cases remains unanalyzed, is Shellsort. Let h be a t-component vector of positive integers. An h-Shellsort will sort any given n elements in t passes, by means of comparisons and exchanges of elements. Let S>j(h; n) denote the average number of element exchanges in the jth pass, assuming that all the n! initial orderings are equally likely. In this paper we derive asymptotic formulas of Sj(h; n) for any fixed h = (h, k, l), making use of a new combinatorial interpretation of S3. For the special case h = (3, 2, 1), the analysis is further sharpened to yield exact expressions.},
added-at = {2016-11-08T04:37:32.000+0100},
author = {Yao, Andrew Chi-Chih},
biburl = {https://www.bibsonomy.org/bibtex/2e1d7b8a5ae99295691fad1ce3eefbd28/ytyoun},
doi = {10.1016/0196-6774(80)90003-6},
interhash = {ba9c262b4dada93209e5c89173f54c44},
intrahash = {e1d7b8a5ae99295691fad1ce3eefbd28},
issn = {0196-6774},
journal = {Journal of Algorithms},
keywords = {algorithm shellsort sorting},
number = 1,
pages = {14--50},
timestamp = {2016-11-08T08:46:21.000+0100},
title = {An Analysis of $(h, k, 1)$-{Shellsort}},
volume = 1,
year = 1980
}