A Lower Bound on the Average-Case Complexity of Shellsort

الأصل · EN

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 Ω(pn¹ ⁺ 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.