I want to sort a list of
n items with a comparison sort. However, one of the comparisons made by the algorithm will be flipped from what it's supposed to be. Specifically, there is one pair of items for which the comparator function consistently gives the wrong result.
What is a efficient
n*log(n) sorting algorithm that will be robust to this faulty comparison? By robust, I mean that every item is off by at most
k spots from its true position, for some reasonably small
If possible, I'd like it to be robust in the worst case (faulty comparison chosen adversarially), but I'll settle for robust in the average case.
An example robust algorithm (that's not efficient), would be to make all
n*(n-1)/2 pairwise comparisons, and place each item by how many of the comparisons they won. Then, no matter what comparison the adversary makes, each items index will be off by no more than
An example of a NON-robust algorithm is quicksort, because the adversary could just choose the largest item to be on the wrong side of the first pivot, making it on average
n/2 spots off from its correct index.