On the distribution of binary search trees under the random permutation model
Random Structures & Algorithms
Large deviations for quicksort
Journal of Algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Approximating the limiting quicksort distribution
Random Structures & Algorithms - Special issue on analysis of algorithms dedicated to Don Knuth on the occasion of his (100)8th birthday
Rates of convergence for Quicksort
Journal of Algorithms - Analysis of algorithms
Guest Editors' Introduction: The Top 10 Algorithms
Computing in Science and Engineering
Rates of convergence for Quicksort
Journal of Algorithms - Analysis of algorithms
The number of bit comparisons used by Quicksort: an average-case analysis
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Smoothed Analysis of Binary Search Trees and Quicksort under Additive Noise
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Random records and cuttings in binary search trees
Combinatorics, Probability and Computing
Smoothed analysis of left-to-right maxima with applications
ACM Transactions on Algorithms (TALG)
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The number of comparisons Xn used by Quicksort to sort an array of n distinct numbers has mean µn of order n log n and standard deviation of order n. Using different methods, Régnier and Rösler each showed that the normalized variate Yn := (Xn - µn)/n converges in distribution, say to Y; the distribution of Y can be characterized as the unique fixed point with zero mean of a certain distributional transformation.We provide the first rates of convergence for the distribution of Yn to that of Y, using various metrics. In particular, we establish the bound 2n-1/2 in the d2-metric, and the rate O(nε - (1/2)) for Kolmogorov-Smirnov distance, for any positive ε.