Indexing metadata

A Gaussian limit process for optimal FIND algorithms


 
Dublin Core PKP Metadata Items Metadata for this Document
 
1. Title Title of document A Gaussian limit process for optimal FIND algorithms
 
2. Creator Author's name, affiliation, country Henning Sulzbach; INRIA Paris-Rocquencourt; France
 
2. Creator Author's name, affiliation, country Ralph Neininger; Goethe University Frankfurt; Germany
 
2. Creator Author's name, affiliation, country Michael Drmota; TU Vienna; Austria
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) FIND algorithm, Quickselect, complexity, key comparisons, functional limit theorem, contraction method, Gaussian process
 
3. Subject Subject classification 60F17; 68P10; 60G15; 60C05; 68Q25
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2014-01-06
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2933
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-2933
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
15. Rights Copyright and permissions The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.

Summary of the Creative Commons Attribution License

You are free
  • to copy, distribute, display, and perform the work
  • to make derivative works
  • to make commercial use of the work
under the following condition of Attribution: others must attribute the work if displayed on the web or stored in any electronic archive by making a link back to the website of EJP via its Digital Object Identifier (DOI), or if published in other media by acknowledging prior publication in this Journal with a precise citation including the DOI. For any further reuse or distribution, the same terms apply. Any of these conditions can be waived by permission of the Corresponding Author.