Insertion sort is used when number of elements is small. It can also be useful when input array is almost sorted, only few elements are misplaced in complete big array.

Radix Sort

- If we have log2n bits for every digit, the running time of Radix appears to be better than Quick Sort for a wide range of input numbers. The constant factors hidden in asymptotic notation are higher for Radix Sort and Quick-Sort uses hardware caches more effectively. Also, Radix sort uses counting sort as a subroutine and counting sort takes extra space to sort numbers.
- An example is when creating a “suffix array” using the skew DC3 algorithm (Kärkkäinen-Sanders-Burkhardt). The algorithm is only linear-time if the sorting algorithm is linear-time, and radix sort is necessary and useful here because the keys are short by construction (3-tuples of integers).