Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)when quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.AofA.2018.23
URN: urn:nbn:de:0030-drops-89165
URL: https://drops.dagstuhl.de/opus/volltexte/2018/8916/
Fuchs, Michael ; Müller, Noela S. ; Sulzbach, Henning
Refined Asymptotics for the Number of Leaves of Random Point Quadtrees
| pdf-format: |
|
Abstract
In the early 2000s, several phase change results from distributional convergence to distributional non-convergence have been obtained for shape parameters of random discrete structures. Recently, for those random structures which admit a natural martingale process, these results have been considerably improved by obtaining refined asymptotics for the limit behavior. In this work, we propose a new approach which is also applicable to random discrete structures which do not admit a natural martingale process. As an example, we obtain refined asymptotics for the number of leaves in random point quadtrees. More applications, for example to shape parameters in generalized m-ary search trees and random gridtrees, will be discussed in the journal version of this extended abstract.
BibTeX - Entry
@InProceedings{fuchs_et_al:LIPIcs:2018:8916,
author = {Michael Fuchs and Noela S. M{\"u}ller and Henning Sulzbach},
title = {{Refined Asymptotics for the Number of Leaves of Random Point Quadtrees}},
booktitle = {29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)},
pages = {23:1--23:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-078-1},
ISSN = {1868-8969},
year = {2018},
volume = {110},
editor = {James Allen Fill and Mark Daniel Ward},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/8916},
URN = {urn:nbn:de:0030-drops-89165},
doi = {10.4230/LIPIcs.AofA.2018.23},
annote = {Keywords: Quadtree, number of leaves, phase change, stochastic fixed-point equation, central limit theorem, positivity of variance, contraction method}
}
| Keywords: | Quadtree, number of leaves, phase change, stochastic fixed-point equation, central limit theorem, positivity of variance, contraction method | |
| Seminar: | 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018) | |
| Issue date: | 2018 | |
| Date of publication: | 18.06.2018 |
