External-Memory Sorting with Comparison Errors.

We provide several algorithms for sorting an array of n comparable distinct elements subject to probabilistic comparison errors in external memory. In this model, which has been extensively studied in internal-memory settings, the comparison of two elements returns the wrong answer according to a fixed probability, $$p_e<1/2$$ , and otherwise returns the correct answer. The dislocation of an element is the distance between its position in a given (current or output) array and its position in a sorted array. There are various existing algorithms that can be utilized for sorting or near-sorting elements subject to probabilistic comparison errors, but these algorithms do not translate into efficient external-memory algorithms, because they all make heavy use of noisy binary searching. In this paper, we provide new efficient methods that are in the external-memory model for sorting with comparison errors. Our algorithms achieve an optimal number of I/Os, in both cache-aware and cache-oblivious settings.