On the average‐case complexity of Shellsort

We prove a lower bound expressed in the increment sequence on the average‐case complexity of the number of inversions of Shellsort. This lower bound is sharp in every case where it could be checked. A special case of this lower bound yields the general Jiang‐Li‐Vitányi lower bound. We obtain new res...

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Bibliographic Details
Published in:Random structures & algorithms Vol. 52; no. 2; pp. 354 - 363
Main Author: Vitanyi, Paul
Format: Journal Article
Language:English
Published: Hoboken Wiley Subscription Services, Inc 01.03.2018
Subjects:
average‐case complexity
Complexity
Inversions
Kolmogorov complexity
lower bound
Lower bounds
Shellsort
ISSN:1042-9832, 1098-2418
Online Access:Get full text
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Summary:We prove a lower bound expressed in the increment sequence on the average‐case complexity of the number of inversions of Shellsort. This lower bound is sharp in every case where it could be checked. A special case of this lower bound yields the general Jiang‐Li‐Vitányi lower bound. We obtain new results, for example, determining the average‐case complexity precisely in the Yao‐Janson‐Knuth 3‐pass case.
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ISSN:1042-9832
1098-2418
DOI:10.1002/rsa.20737