Refined quicksort asymptotics |
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Authors: | Ralph Neininger |
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Institution: | Institute for Mathematics, J.W. Goethe University Frankfurt, Frankfurt am Main, Germany |
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Abstract: | The complexity of the Quicksort algorithm is usually measured by the number of key comparisons used during its execution. When operating on a list of n data, permuted uniformly at random, the appropriately normalized complexity Yn is known to converge almost surely to a non‐degenerate random limit Y. This assumes a natural embedding of all Yn on one probability space, e.g., via random binary search trees. In this note a central limit theorem for the error term in the latter almost sure convergence is shown: where denotes a standard normal random variable. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 346–361, 2015 |
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Keywords: | quicksort complexity key comparisons central limit theorem strong limit theorem rate of convergence Zolotarev metric contraction method |
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