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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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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
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"... We present a new algorithm, filter tree, for reducing (costsensitive) kclass classification to binary classification. The filter tree is provably consistent, in the sense that given an optimal binary classifier, the reduction yields an optimal multiclass classifier. (The commonly used tree approac ..."
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We present a new algorithm, filter tree, for reducing (costsensitive) kclass classification to binary classification. The filter tree is provably consistent, in the sense that given an optimal binary classifier, the reduction yields an optimal multiclass classifier. (The commonly used tree approach is provably inconsistent.) The filter tree is robust. It suffers multiclass regret at most log 2 k times the binary regret. The filter tree can also be used for costsensitive multiclass classification, where each prediction may have a different associated loss. The resulting regret bound is superior to the guarantees provided by all previous methods. 1
Breaking the Θ(n log² n) Barrier for Sorting with Faults
, 1997
"... In this paper, we study the problem of constructing a sorting circuit, network, or PRAM algorithm that is tolerant to faults. For the most part, we focus on fault patterns that are random, i.e., where the result of each comparison is independently faulty with probability upperbounded by some con ..."
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In this paper, we study the problem of constructing a sorting circuit, network, or PRAM algorithm that is tolerant to faults. For the most part, we focus on fault patterns that are random, i.e., where the result of each comparison is independently faulty with probability upperbounded by some constant. All previous faulttolerant sorting circuits, networks, and parallel algorithms require\Omega\Gammaqui 2 n) depth and/or\Omega\Gamma n log 2 n) comparisons to sort n items. In this paper, we construct: ffl a passivefaulttolerant sorting circuit with O(n log n log log n) comparators, thereby answering a question posed by Yao and Yao in 1985, ffl a reversalfaulttolerant sorting network with O(n log log 2 3 n) comparators, thereby answering a question posed by Assaf and Upfal in 1990, and ffl a deterministic O(log n)step O(n)processor EREW PRAM faulttolerant sorting algorithm, thereby answering a question posed by Feige, Peleg, Raghavan, and Upfal in 1990. The r...