Abstract.
We analyze the Shell Sort algorithm under the usual random permutation model. Using empirical distribution functions, we recover Louchard's result that the running time of the 1-stage of (2,1) -Shell Sort has a limiting distribution given by the area under the absolute Brownian bridge. The analysis extends to (h,1) -Shell Sort where we find a limiting distribution given by the sum of areas under correlated absolute Brownian bridges. A variation of (h,1) -Shell Sort which is slightly more efficient is presented and its asymptotic behavior analyzed.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received June 6, 2000; revised September 27, 2000.
Rights and permissions
About this article
Cite this article
Smythe, R., Wellner, J. Stochastic Analysis of Shell Sort. Algorithmica 31, 442–457 (2001). https://doi.org/10.1007/s00453-001-0048-0
Issue Date:
DOI: https://doi.org/10.1007/s00453-001-0048-0