Geodesic
Geometric Bucket Trees: Analysis of Linear Bucket Tree
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10) (2010).

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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 $y$. 
@article{DMTCS_2010_special_258_a0,
     author = {Jacquet, Philippe and Muhlethaler, Paul},
     title = {Geometric {Bucket} {Trees:} {Analysis} of {Linear} {Bucket} {Tree}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10)},
     year = {2010},
     doi = {10.46298/dmtcs.2764},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2764/}
}
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Jacquet, Philippe; Muhlethaler, Paul. Geometric Bucket Trees: Analysis of Linear Bucket Tree. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10) (2010). doi : 10.46298/dmtcs.2764. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2764/

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