A perturbation technique can be used to simplify and sharpen A. C. Yao's theorems about the behavior of shellsort with increments (h; g; 1). In particular, when h = (n 7=15) and g = (h 1=5), the average running time is O(n 23=15). The proof involves interesting properties of the inversions in random permutations that have been h-sorted and g-sorted. Shellsort, also known as the \diminishing inc...
