Sorting with Recurrent Comparison Errors

TL;DR

This paper introduces a sorting algorithm designed for environments with recurrent random comparison errors, achieving optimal bounds on dislocation while maintaining efficient runtime.

Contribution

It presents a new sorting algorithm that handles recurrent random comparison errors with proven optimal bounds on dislocation and runtime.

Findings

Runs in O(n^2) time

Maximum dislocation is O(log n)

Total dislocation is O(n)

Abstract

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.