Sorting with Recurrent Comparison Errors
Barbara Geissmann, Stefano Leucci, Chih-Hung Liu, Paolo Penna

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 distinct elements in this model. In particular, it runs in time, the maximum dislocation of the elements in the output is , while the total dislocation is . These guarantees are the best possible since we prove that even randomized algorithms cannot achieve maximum dislocation with high probability, or total dislocation in expectation, regardless of their running time.
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Taxonomy
TopicsRandom Matrices and Applications · Probability and Risk Models · Bayesian Methods and Mixture Models
