Sorting with Recurrent Comparison Errors

We present a sorting algorithm for the case of recurrent random comparison errors. The algorithm essentially achieves simultaneously good properties of previous algorithms for sorting n distinct elements in this model. In particular, it runs in O(n^2) time, the maximum dislocation of the elements in the output is O(log n), while the total dislocation is O(n). These guarantees are the best possible since we prove that even randomized algorithms cannot achieve o(log n) maximum dislocation with high probability, or o(n) total dislocation in expectation, regardless of their running time.