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Transitional Behaviors of the Average Cost of Quicksort With Medianof(2t + 1)
, 2001
"... A fine analysis is given of the transitional behavior of the average cost of quicksort with medianofthree. Asymptotic formulae are derived for the stepwise improvement of the average cost of quicksort when iterating medianofthree k rounds for all possible values of k. The methods used are genera ..."
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Cited by 11 (6 self)
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A fine analysis is given of the transitional behavior of the average cost of quicksort with medianofthree. Asymptotic formulae are derived for the stepwise improvement of the average cost of quicksort when iterating medianofthree k rounds for all possible values of k. The methods used are general enough to apply to quicksort with medianof(2t + 1) and to explain in a precise manner the transitional behaviors of the average cost from insertion sort to quicksort proper. Our results also imply nontrivial bounds on the expected height, "saturation level", and width in a random locally balanced binary search tree.
Approximate Sorting ⋆
"... Abstract. We show that any randomized algorithm to approximate any given ranking of n items within expected Spearman’s footrule distance n 2 /ν(n) needs at least n (min{log ν(n), log n} − 6) comparisons. This bound is tight up to a constant factor since there exists a deterministic algorithm that s ..."
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Abstract. We show that any randomized algorithm to approximate any given ranking of n items within expected Spearman’s footrule distance n 2 /ν(n) needs at least n (min{log ν(n), log n} − 6) comparisons. This bound is tight up to a constant factor since there exists a deterministic algorithm that shows that 6n(log ν(n) + 1) comparisons are always sufficient. Keywords. Sorting, Ranking, Spearman’s footrule metric, Kendall’s tau metric
IOS Press Approximate Sorting
"... Abstract. We show that any comparison based, randomized algorithm to approximate any given ranking of n items within expected Spearman’s footrule distance n 2 /ν(n) needs at least n (min{log ν(n), log n} − 6) comparisons in the worst case. This bound is tight up to a constant factor since there exi ..."
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Abstract. We show that any comparison based, randomized algorithm to approximate any given ranking of n items within expected Spearman’s footrule distance n 2 /ν(n) needs at least n (min{log ν(n), log n} − 6) comparisons in the worst case. This bound is tight up to a constant factor since there exists a deterministic algorithm that shows that 6n log ν(n) comparisons are always sufficient. Keywords: