On The Average-Case Complexity of Shellsort

Abstract

We prove a lower bound expressed in the increment sequence on the average-case complexity of the number of inversions of Shellsort. This lower bound is sharp in every case where it could be checked. A special case of this lower bound yields the general Jiang-Li-Vit\'anyi lower bound. We obtain new results e.g. determining the average-case complexity precisely in the Yao-Janson-Knuth 3-pass case.