Shellsort with three increments

Svante Janson; Donald E. Knuth

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arXiv · cs/9608105

Shellsort with three increments

Svante Janson·Donald E. Knuth

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Abstract

A perturbation technique can be used to simplify and sharpen A. C. Yao's theorems about the behavior of shellsort with increments $(h,g,1)$. In particular, when $h=Θ(n^{7/15})$ and $g=Θ(h^{1/5})$, the average running time is $O(n^{23/15})$. The proof involves interesting properties of the inversions in random permutations that have been $h$-sorted and $g$-sorted.

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Svante Janson, Donald E. Knuth. 1996-08-22. Shellsort with three increments. https://arxiv.org/abs/cs/9608105

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