We prove a lower bound expressed in the increment se- quence 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-Vitányi lower bound. We obtain new results, for example, determining the average- case complexity precisely in the Yao-Janson-Knuth 3-pass case.

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Random Structures & Algorithms
CWI management

Vitányi, P.M.B. (2018). On the average-case complexity of Shellsort. Random Structures & Algorithms, 52(2), 354–363. doi:10.1002/rsa.20737