Fast Exchange Sorts 1

We present three variations of the following new sorting theme: Throughout the sort, the array is maintained in piles of sorted elements. At each step, the piles are split into two parts, so that the elements of the left piles are smaller than (or equal to) the elements of the right piles. Then, the two parts are each sorted, recursively. The theme, then, is a combination of Hoare's Quicksort idea, and the Pick algorithm, by Blum, et al., for linear selection. The variations arise from the possible choices of splitting method. Two variations attempt to minimize the average number of comparisons. The better of these has an average performance of 1:075n lg n comparisons. The third variation sacriices the average case for a worst-case performance of 1:756n lg n, which is better than Heapsort. They all require minimal extra space and about as many data moves as comparisons.