Randomized algorithms and pseudorandom numbers
Journal of the ACM (JACM)
Pseudorandomness and Cryptographic Applications
Pseudorandomness and Cryptographic Applications
Generating Quasi-Random Sequences From Slightly-Random Sources
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
DIALM-POMC '05 Proceedings of the 2005 joint workshop on Foundations of mobile computing
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The worst-case complexity of an implementation of Quicksort depends on the random source that is used to select the pivot elements. In this paper we estimate the expected number of comparisons of Quicksort as a function of the entropy of the random source. We give upper and lower bounds and show that the expected number of comparisons increases from nlog n to n2, if the entropy of the random source is bounded. As examples we show explicit bounds for distributions with bounded min-entropy and the geometrical distribution, as well as an upper bound when using a δ-random source.