# Geometric Bucket Trees: Analysis of Linear Bucket Tree

1 HIPERCOM - High performance communication
Inria Paris-Rocquencourt, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR
Abstract : We analyse the average number of buckets in a Linear Bucket tree created by $n$ points uniformly dispatched on an interval of length $y$. A new bucket is created when a point does not fall in an existing bucket. The bucket is the interval of length 2 centered on the point. We illustrate this concept by an interesting tale of how the moon's surface took on its present form. Thanks to an explicit Laplace transform of the Poissonized sequence, and the use of dePoissonization tools, we obtain the explicit asymptotic expansions of the average number of buckets in most of the asymptotic regimes relative to $n$ and $y$.
Keywords :
Document type :
Conference papers
Domain :

Cited literature [11 references]

https://hal.inria.fr/hal-01185562
Contributor : Coordination Episciences Iam <>
Submitted on : Thursday, August 20, 2015 - 4:31:51 PM
Last modification on : Wednesday, September 16, 2020 - 5:10:15 PM
Long-term archiving on: : Wednesday, April 26, 2017 - 9:56:28 AM

### File

dmAM0128.pdf
Publisher files allowed on an open archive

### Identifiers

• HAL Id : hal-01185562, version 1

### Citation

Philippe Jacquet, Paul Muhlethaler. Geometric Bucket Trees: Analysis of Linear Bucket Tree. 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), 2010, Vienna, Austria. pp.401-414. ⟨hal-01185562⟩

Record views