On selecting the largest element in spite of erroneous information
4th Annual Symposium on Theoretical Aspects of Computer Sciences on STACS 87
Fault tolerant sorting networks
SIAM Journal on Discrete Mathematics
Comparison-based search in the presence of errors
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Computing with Noisy Information
SIAM Journal on Computing
Searching games with errors---fifty years of coping with liars
Theoretical Computer Science
Introduction to Algorithms
Constant time parallel sorting: an empirical view
Journal of Computer and System Sciences
Sorting and searching in the presence of memory faults (without redundancy)
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Noisy binary search and its applications
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
ACM SIGACT News
The Bayesian Learner is Optimal for Noisy Binary Search (and Pretty Good for Quantum as Well)
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Journal of Computer and System Sciences
Optimal resilient sorting and searching in the presence of memory faults
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
ESA'11 Proceedings of the 19th European conference on Algorithms
Max algorithms in crowdsourcing environments
Proceedings of the 21st international conference on World Wide Web
The Journal of Machine Learning Research
So who won?: dynamic max discovery with the crowd
SIGMOD '12 Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data
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In experimental psychology, the method of paired comparisons was proposed as a means for ranking preferences amongst n elements of a human subject. The method requires performing all $\binom{n}{2}$ comparisons then sorting elements according to the number of wins. The large number of comparisons is performed to counter the potentially faulty decision-making of the human subject, who acts as an imprecise comparator. We consider a simple model of the imprecise comparisons: there exists some *** 0 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 *** corresponds to the just noticeable difference unit (JND) or difference threshold in the psychophysics literature, but does not require the statistical assumptions used to define this value. In this model, the standard method of paired comparisons minimizes the errors introduced by the imprecise comparisons at the cost of $\binom{n}{2}$ comparisons. We show that the same optimal guarantees can be achieved using 4 n 3/2 comparisons, and we prove the optimality of our method. We then explore the general tradeoff between the guarantees on the error that can be made and number of comparisons for the problems of sorting, max-finding, and selection. Our results provide close-to-optimal solutions for each of these problems.