Best sorting algorithm for nearly sorted lists

Abstract

Straight Insertion Sort, Shellsort, Straight Merge Sort, Quickersort, and Heapsort are compared on nearly sorted lists. The ratio of the minimum number of list elements which must be removed so that the remaining portion of the list is in order to the size of the list is the authors' measure of sortedness. Tests on randomly generated lists of various combinations of list length and small sortedness ratios indicate that Straight Insertion Sort is best for small or very nearly sorted lists and that Quickersort is best otherwise. Cook and Kim also show that a combination of the Straight Insertion Sort and Quickersort with merging yields a sorting method that performs as well as or better than either Straight Insertion Sort or Quickersort on nearly sorted lists.