A Lower Bound on the Average-Case Complexity of Shellsort

Tao Jiang; Ming Li; Paul Vitanyi

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A Lower Bound on the Average-Case Complexity of Shellsort

Tao Jiang·Ming Li·Paul Vitanyi

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Abstract

We prove a general lower bound on the average-case complexity of Shellsort: the average number of data-movements (and comparisons) made by a $p$-pass Shellsort for any incremental sequence is $\Omega (pn^{1 + 1/p})$ for every $p$. The proof method is an incompressibility argument based on Kolmogorov complexity. Using similar techniques, the average-case complexity of several other sorting algorithms is analyzed.

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Tao Jiang, Ming Li, Paul Vitanyi. 1999-06-04. A Lower Bound on the Average-Case Complexity of Shellsort. https://arxiv.org/abs/cs/9906008

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