  Recently, many results on the computational complexity of sorting algorithms
were obtained using Kolmogorov complexity (the incompressibility method).
Especially, the usually hard average-case analysis is ammenable to this method.
Here we survey such results about Bubblesort, Heapsort, Shellsort,
Dobosiewicz-sort, Shakersort, and sorting with stacks and queues in sequential
or parallel mode. Especially in the case of Shellsort the uses of Kolmogorov
complexity surprisingly easily resolved problems that had stayed open for a
long time despite strenuous attacks.
