Sorting and Selection with Imprecise Comparisons
Miklos Ajtai, Vitaly Feldman, Avinatan Hassidim, Jelani Nelson

TL;DR
This paper studies algorithms for sorting and selection under imprecise comparisons, establishing optimal methods that balance accuracy and comparison complexity, inspired by human judgment and adversarial errors.
Contribution
It introduces a model of imprecise comparisons, proves optimality of the paired comparison method, and develops near-optimal algorithms for sorting and selection with fewer comparisons.
Findings
Paired comparison method is optimal but comparison-intensive.
Achieves the same accuracy with only 4 n^{3/2} comparisons.
Provides lower bounds and near-optimal algorithms for sorting and selection.
Abstract
We consider a simple model of imprecise comparisons: there exists some such that when a subject is given two elements to compare, if the values of those elements (as perceived by the subject) differ by at least , then the comparison will be made correctly; when the two elements have values that are within , the outcome of the comparison is unpredictable. This model is inspired by both imprecision in human judgment of values and also by bounded but potentially adversarial errors in the outcomes of sporting tournaments. Our model is closely related to a number of models commonly considered in the psychophysics literature where corresponds to the {\em just noticeable difference unit (JND)} or {\em difference threshold}. In experimental psychology, the method of paired comparisons was proposed as a means for ranking preferences amongst elements of a…
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Taxonomy
TopicsBayesian Modeling and Causal Inference · Rough Sets and Fuzzy Logic · Imbalanced Data Classification Techniques
