Translator Disclaimer
2014 A Gaussian limit process for optimal FIND algorithms
Henning Sulzbach, Ralph Neininger, Michael Drmota
Author Affiliations +
Electron. J. Probab. 19(none): 1-28 (2014). DOI: 10.1214/EJP.v19-2933

Abstract

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.

Citation

Download Citation

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

Information

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

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

JOURNAL ARTICLE
28 PAGES


SHARE
Vol.19 • 2014
Back to Top