Question

For general-purpose sorting, the answer appears to be no, as quick sort, merge sort and heap sort tend to perform better in the average- and worst-case scenarios. However, insertion sort appears to excel at incremental sorting, that is, adding elements to a list one at a time over an extended period of time while keeping the list sorted, especially if the insertion sort is implemented as a linked list (O(log n) average case vs. O(n)). However, a heap seems to be able to perform just (or nearly) as well for incremental sorting (adding or removing a single element from a heap has a worst-case scenario of O(log n)). So what exactly does insertion sort have to offer over other comparison-based sorting algorithms or heaps?

Answer 1

From http://www.sorting-algorithms.com/insertion-sort:

Although it is one of the elementary sorting algorithms with
O(n²) worst-case time, insertion sort
is the algorithm of choice either when
the data is nearly sorted (because it
is adaptive) or when the problem size
is small (because it has low
overhead).

For these reasons, and because it is also stable, insertion sort is
often used as the recursive base case
(when the problem size is small) for
higher overhead divide-and-conquer
sorting algorithms, such as merge sort
or quick sort.