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2014 A Gaussian limit process for optimal FIND algorithms
Henning Sulzbach, Ralph Neininger, Michael Drmota
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Electron. J. Probab. 19: 1-28 (2014). DOI: 10.1214/EJP.v19-2933


We consider versions of the FIND algorithm where the pivot element used is the median of a subset chosen uniformly at random from the data. For the median selection we assume that subsamples of size asymptotic to $c \cdot n^\alpha$ are chosen, where $0 < \alpha \leq \frac{1}{2}$, $c > 0$ and $n$ is the size of the data set to be split. We consider the complexity of FIND as a process in the rank to be selected and measured by the number of key comparisons required. After normalization we show weak convergence of the complexity to a centered Gaussian process as $n \to \infty$, which depends on $\alpha$. The proof relies on a contraction argument for probability distributions on càdlàg functions. We also identify the covariance function of the Gaussian limit process and discuss path and tail properties.


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Henning Sulzbach. Ralph Neininger. Michael Drmota. "A Gaussian limit process for optimal FIND algorithms." Electron. J. Probab. 19 1 - 28, 2014.


Accepted: 6 January 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1358.68085
MathSciNet: MR3164756
Digital Object Identifier: 10.1214/EJP.v19-2933

Primary: 60F17
Secondary: 60C05 , 60G15 , 68P10 , 68Q25

Keywords: Complexity , contraction method , FIND algorithm , Functional limit theorem , Gaussian process , key comparisons , QuickSelect


Vol.19 • 2014
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