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16
Error Correcting Tournaments
, 2008
"... Abstract. We present a family of adaptive pairwise tournaments that are provably robust against large error fractions when used to determine the largest element in a set. The tournaments use nk pairwise comparisons but have only O(k + log n) depth, where n is the number of players and k is the robus ..."
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Cited by 26 (4 self)
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Abstract. We present a family of adaptive pairwise tournaments that are provably robust against large error fractions when used to determine the largest element in a set. The tournaments use nk pairwise comparisons but have only O(k + log n) depth, where n is the number of players and k is the robustness parameter (for reasonable values of n and k). These tournaments also give a reduction from multiclass to binary classification in machine learning, yielding the best known analysis for the problem. 1
Max Algorithms in Crowdsourcing Environments
"... Our work investigates the problem of retrieving the maximum item from a set in crowdsourcing environments. We first develop parameterized families of max algorithms, that take as input a set of items and output an item from the set that is believed to be the maximum. Such max algorithms could, for i ..."
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Our work investigates the problem of retrieving the maximum item from a set in crowdsourcing environments. We first develop parameterized families of max algorithms, that take as input a set of items and output an item from the set that is believed to be the maximum. Such max algorithms could, for instance, select the best Facebook profile that matches a given person or the best photo that describes a given restaurant. Then, we propose strategies that select appropriatemaxalgorithmparameters. Ourframeworksupports various human error and cost models and we consider many of them for our experiments. We evaluate under many metrics, both analytically and via simulations, the tradeoff between three quantities: (1) quality, (2) monetary cost, and (3) execution time. Also, we provide insights on the effectiveness of the strategies in selecting appropriate max algorithm parameters and guidelines for choosing max algorithms and strategies for each application.
Sorting and Selection with Imprecise Comparisons
"... Abstract. 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 ( n 2 comparisons then sorting elements according to the number of wins. The large number of comparisons i ..."
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Abstract. 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 ( n 2 comparisons then sorting elements according to the number of wins. The large number of comparisons is performed to counter the potentially faulty decisionmaking of the human subject, who acts as an imprecise comparator. We consider a simple model of the imprecise comparisons: there exists some δ> 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 δ, then the comparison will be made correctly; when the two elements have values that are within δ, the outcome of the comparison is unpredictable. This δ 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 ( n 2 comparisons. We show that the same optimal guarantees can be achieved using 4n 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, maxfinding, and selection. Our results provide closetooptimal solutions for each of these problems. 1
Robustness versus Performance in Sorting and Tournament Algorithms
"... Abstract: In this paper we analyze the robustness of sorting and tournament algorithms against faulty comparisons. Sorting algorithms are differently affected by faulty comparisons depending on how comparison errors can affect the overall result. In general, there exists a tradeoff between the numbe ..."
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Abstract: In this paper we analyze the robustness of sorting and tournament algorithms against faulty comparisons. Sorting algorithms are differently affected by faulty comparisons depending on how comparison errors can affect the overall result. In general, there exists a tradeoff between the number of comparisons and the accuracy of the result, but some algorithms like Merge Sort are Paretodominant over others. For applications, where the accuracy of the top rankings is of higher importance than the lower rankings, tournament algorithms such as the Swiss System are an option. Additionally, we propose a new tournament algorithm named Iterated Knockout Systems which is less exact but more efficient than the Swiss Systems.
The Importance of Being Expert: Efficient MaxFinding in Crowdsourcing For reviewing purposes only. Please do not distribute!
"... Οὐ piάνυ ἡμῖν οὕτω φροντιστέον τί ἐροῦσιν οἱ piολλοὶ ἡμᾶς, ..."
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Οὐ piάνυ ἡμῖν οὕτω φροντιστέον τί ἐροῦσιν οἱ piολλοὶ ἡμᾶς,
Sorting and Searching With a Faulty Comparison Oracle
, 1992
"... this paper, we follow usual convention of denoting the base 2 logarithm by log and the natural logarithm by ln. ..."
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this paper, we follow usual convention of denoting the base 2 logarithm by log and the natural logarithm by ln.
Group Testing with Unreliable Tests
, 1996
"... We consider the problem of locating two unknown elements x; y using group testing devices. Assuming that up to a given number E of tests out of Q can give erroneous feedback, we provide optimal algorithms to search for x and y. 1 Introduction The problem of coping with erroneous information in sear ..."
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We consider the problem of locating two unknown elements x; y using group testing devices. Assuming that up to a given number E of tests out of Q can give erroneous feedback, we provide optimal algorithms to search for x and y. 1 Introduction The problem of coping with erroneous information in search procedures has recently received considerable attention by several researchers (eg., [1, 4, 5, 6, 15, 16, 17, 18, 19, 20, 21, 23]). All previous papers considered the problem of searching an unknown number in a set when a given number of queries may receive erroneous answer. In this paper we consider the analogous problem when one searches for two elements. Our motivations are similar to that of Hwang [12] who noticed a kind of "discontinuity" in the difficulty of finding optimal search procedures when the problem is that of searching for more than one object. More precisely, we consider the problem of identifying two distinguished elements x and y in a search space S by testing subsets ...
Minimum and maximum against k lies∗
"... Abstract: A neat 1972 result of Pohl asserts that d3n/2e−2 comparisons are sufficient, and also necessary in the worst case, for finding both the minimum and the maximum of an nelement totally ordered set. The set is accessed via an oracle for pairwise comparisons. More recently, the problem has be ..."
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Abstract: A neat 1972 result of Pohl asserts that d3n/2e−2 comparisons are sufficient, and also necessary in the worst case, for finding both the minimum and the maximum of an nelement totally ordered set. The set is accessed via an oracle for pairwise comparisons. More recently, the problem has been studied in the context of the Rényi–Ulam liar games, where the oracle may give up to k false answers. For large k, an upper bound due to Aigner shows that (k+O( k))n comparisons suffice. We improve on this by providing an algorithm with at most (k + 1+C)n+O(k3) comparisons for some constant C. A recent result of Pálvölgyi provides a lower bound of the form (k+1+0.5)n−Dk, so our upper bound for the coefficient of n is tight up to the value of C. Key words and phrases: computing the minimum and maximum, computation against lies, number of comparisons, liar games, computation in the presence of errors 1