A Lower Bound on the Average-Case Complexity of Shellsort

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 $\Omega (p{n}^{1+1/p})$ 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.

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