Lower Bounds for Shellsort

We show lower bounds on the worst-case complexity of Shellsort. In particular, we give a fairly simple proof of an Ω(n(lg2n)/(lglgn)2) lower bound for the size of Shellsort sorting networks for arbitrary increment sequences. We also show an identical lower bound for the running time of Shellsort alg...

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Bibliographic Details
Published inJournal of algorithms Vol. 23; no. 2; pp. 221 - 240
Main Authors Plaxton, C.Greg, Suel, Torsten
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 01.05.1997
Elsevier
Subjects
Algorithmics. Computability. Computer arithmetics
Applied sciences
Computer science; control theory; systems
Exact sciences and technology
Theoretical computing
Lower bound
Algorithms
Algorithm complexity
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Summary:We show lower bounds on the worst-case complexity of Shellsort. In particular, we give a fairly simple proof of an Ω(n(lg2n)/(lglgn)2) lower bound for the size of Shellsort sorting networks for arbitrary increment sequences. We also show an identical lower bound for the running time of Shellsort algorithms, again for arbitrary increment sequences. Our lower bounds establish an almost tight trade-off between the running time of a Shellsort algorithm and the length of the underlying increment sequence.
ISSN:0196-6774
1090-2678
DOI:10.1006/jagm.1996.0825