Strong concentration for Quicksort

Authors:
Colin McDiarmid;Ryan Hayward
Affiliations:
-;-
Venue:
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Year:
1992

Citing 3
Cited 1

A note on the height of binary search trees

Journal of the ACM (JACM)
Increasing the efficiency of quicksort

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Algorithm 64: Quicksort

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Martingales on trees and the empire chromatic number of random trees

FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory

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Abstract

Let Qn be the random number of comparisons made by quicksort in sorting n distinct keys, when we assume that all n! possible orderings are equally likely. Known results concerning moments for Qn do not show how rare it is for Qn to make large deviations from its mean. Here we give a good approximation to the probability of such a large deviation, and find that this probability is quite small. As well as the basic quicksort we consider the variant in which the partitioning key is chosen as the median of (2t+1) keys.