Insertion sort: Encyclopedia II - Insertion sort - Variants

Insertion sort - Variants

D.L. Shell made substantial improvements to the algorithm, and the modified version is called Shell sort. It compares elements separated by a distance that decreases on each pass. Shellsort has distinctly improved running times in practical work, with two simple variants requiring O(n^3/2) and O(n^4/3) time.

If comparisons are very costly compared to swaps, as is the case for example with string keys stored by reference, then using binary insertion sort can be a good strategy. Binary insertion sort employs binary search to find the right place to insert new elements, and therefore performs comparisons in the worst case, which is Θ(n log n). The algorithm as a whole still takes Θ(n²) time on average due to the series of swaps required for each insertion, and since it always uses binary search, the best case is no longer O(n) but O(n log n).

To avoid having to make a series of swaps for each insertion, we could instead store the input in a linked list, which allows us to insert and delete elements in constant time. Unfortunately, binary search on a linked list is impossible, so we still spend Ω(n²) time searching. If we instead replace it by a more sophisticated data structure such as a heap or binary tree, we can significantly decrease both search and insert time. This is the essence of heap sort and binary tree sort.

In 2004, Bender, Farach-Colton, and Mosteiro published a new variant of insertion sort called library sort or gapped insertion sort that leaves a small number of unused spaces ("gaps") spread throughout the array. The benefit is that insertions need only shift elements over until a gap is reached. Surprising in its simplicity, they show that this sorting algorithm runs with high probability in O(n log n) time. [1]

Adapted from the Wikipedia article "Variants", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki