• Corpus ID: 3054966

An Analysis of (h,k,l) -shellsort By

@inproceedings{Yao1998AnAO,
  title={An Analysis of (h,k,l) -shellsort By},
  author={Andrew Chi-Chih Yao},
  year={1998}
}

• A. Yao
• Published 1998
• Mathematics

One classical sorting algorithm, whose performance in many cases remains unanalyzed, is Shellsort. Let ?i be a t-component vector of positive integers. An z-Shellsort will sort any given n elements in t passes, by means of comparisons and exchanges of elements. Let S;(c;n) denote the average number of element exchanges in the j-th J pass, assuming that all the n! initial orderings are equally likely. In this paper we derive asymptotic formulas of Sj(<;n) for any fixed h' = (h,k,l) , making use of a new combinatorial interpretation of S 3 . For the special case h'= (3&l) , the analysis is further sharpened to yield exact expressions. f * This work was supported in part by National Science Foundation under grant MCS77-05313. Part of this work was done while the author was on leave at Bell Laboratories, 600 Mountain Avenue, Murray Hill, New Jersey 079'7%.