Shellsort with three increments
Svante Janson, Donald E. Knuth

TL;DR
This paper refines theoretical understanding of Shellsort with three specific increments, demonstrating an average-case running time of O(n^{23/15}) through a novel perturbation approach and analysis of permutation inversions.
Contribution
It introduces a perturbation technique to improve and clarify Yao's theorems for Shellsort with increments (h,g,1), establishing new average-case complexity bounds.
Findings
Average running time is O(n^{23/15}) for specific increments
Perturbation technique simplifies analysis of permutation inversions
Provides sharper bounds on Shellsort performance with three increments
Abstract
A perturbation technique can be used to simplify and sharpen A. C. Yao's theorems about the behavior of shellsort with increments . In particular, when and , the average running time is . The proof involves interesting properties of the inversions in random permutations that have been -sorted and -sorted.
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Taxonomy
TopicsStructural Analysis and Optimization
