Stochastic Analysis of Shell Sort

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.