@inproceedings{7dd19f0010a644f8a06d27c6db94e65c,

title = "Tight lower bounds for Shellsort",

abstract = "Shellsort is a simple classic algorithm that runs competitively on both mid-sized and nearly sorted files. It uses an increment sequence, the choice of which can drastically affect the algorithm's running time. Due to the results of Pratt, the running time of Shellsort was long thought to be Θ(N3/2) for increment sequences that are “almost geometric”. However, recent results have lowered the upper bound substantially, although the new bounds were not known to be tight. In this paper, we show that an increment sequence given by Sedgewick is Θ(N4/3) by analyzing the time required to sort a particularly bad permutation. Extending this proof technique to various increment sequences seems to lead to lower bounds that in general match the known upper bounds and suggests that Shellsort runs in Ω(N1 + ∈/→log N) for increment sequences of practical interest, and that no increment sequence exists that would make Shellsort optimal.",

author = "Weiss, {Mark Allen} and Robert Sedgewick",

year = "1988",

month = jan,

day = "1",

doi = "10.1007/3-540-19487-8_29",

language = "English (US)",

isbn = "9783540194873",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "255--262",

editor = "Rolf Karlsson and Andrzej Lingas",

booktitle = "SWAT 88 - 1st Scandinavian Workshop on Algorithm Theory, Proceedings",

address = "Germany",

note = "1st Scandinavian Workshop on Algorithm Theory, SWAT 1988 ; Conference date: 05-07-1988 Through 08-07-1988",

}