A Lower Bound on the Average-Case Complexity of Shellsort

Tao Jiang; Ming Li; Paul Vitanyi

A Lower Bound on the Average-Case Complexity of Shellsort

Computational Complexity 2015-01-29 v2 Data Structures and Algorithms

Authors: Tao Jiang , Ming Li , Paul Vitanyi

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.

Keywords

approximation algorithm

Cite

@article{arxiv.cs/9906008,
  title  = {A Lower Bound on the Average-Case Complexity of Shellsort},
  author = {Tao Jiang and Ming Li and Paul Vitanyi},
  journal= {arXiv preprint arXiv:cs/9906008},
  year   = {2015}
}

Comments

Preliminary version 10 pages, 2 figures, Proc ICALP 99, Springer LNCS; final version (given here) LaTeX 5 pages published in J. Assoc. Comp. Mach. as below

A Lower Bound on the Average-Case Complexity of Shellsort

Abstract

Keywords

Cite

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