# Analysis of Pivot Sampling in Dual-Pivot Quicksort: A Holistic Analysis of Yaroslavskiy’s Partitioning Scheme

```@article{Wild2015AnalysisOP,
title={Analysis of Pivot Sampling in Dual-Pivot Quicksort: A Holistic Analysis of Yaroslavskiy’s Partitioning Scheme},
author={Sebastian Wild and Markus E. Nebel and Conrado Mart'inez},
journal={Algorithmica},
year={2015},
volume={75},
pages={632-683}
}```
• Published 29 November 2014
• Computer Science
• Algorithmica
The new dual-pivot Quicksort by Vladimir Yaroslavskiy—used in Oracle’s Java runtime library since version 7—features intriguing asymmetries. [] Key Method Consequently, we take a more holistic approach and give also the precise leading term of the average number of swaps, the number of executed Java Bytecode instructions and the number of scanned elements, a new simple cost measure that approximates I/O costs in the memory hierarchy. We determine optimal order statistics for each of the cost measures. It…
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Surprisingly, Yaroslavskiy's algorithm needs sightly more Bytecode instructions than a simple implementation of classic Quicksort—contradicting observed running times; and it is shown that the (suitably normalized) costs of YaroslavSKY's algorithm converge to a random variable whose distribution is characterized by a fixed-point equation.
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ArXiv
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It is shown that the (suitably normalized) costs of Yaroslavskiy’s algorithm converge to a random variable whose distribution is characterized by a fix point equation that for large n, costs are concentrated about their mean.
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