Improved upper bounds on shellsort

The running time of Shellsort, with the number of passes restricted to O(log N), was thought for some time to be Θ(N3/2), due to general results of Pratt. Sedgewick recently gave an O(N4/3) bound, but extensions of his method to provide better bounds seem to require new results on a classical problem in number theory. In this paper, we use a different approach to achieve O(N1+4/√2lgN).