Abstract

. 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 = \Theta(n 7=15 ) and g = \Theta(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 increment sort" [7, Algorithm 5.2.1D], puts the elements of an array (X 0 ; : : : ; X n\Gamma1 ) into order by successively performing a straight insertion sort on larger and larger subarrays of equally spaced elements. The algorithm consists of t passes defined by increments (h t\Gamma1 ; : : : ; h 1 ; h 0 ), where h 0 = 1; the jth pass makes X k X l whenever l \Gamma k = h t\Gammaj . A. C. Yao [11] has analyzed the average behavior of shellsort in the general three-pass case when the increments are (h; g; 1). The most interesting part of his analysis dealt with the third ...

Citations