Výsledky vyhledávání - "Philippe Flajolet"

Akademický článek

The height of random binary unlabelled trees

Autor: Nicolas Broutin, Philippe Flajolet

Publikováno v: Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings vol. AI,..., Iss Proceedings (2008)

This extended abstract is dedicated to the analysis of the height of non-plane unlabelled rooted binary trees. The height of such a tree chosen uniformly among those of size $n$ is proved to have a limiting theta distribution, both in a central and l

Externí odkaz: https://doaj.org/article/5fe341b86eb24d3cafb7fa5dfb86dd39

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Akademický článek

Analytic Combinatorics of the Mabinogion Urn

Autor: Philippe Flajolet, Thierry Huillet

Publikováno v: Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings vol. AI,..., Iss Proceedings (2008)

The Mabinogion urn is a simple model of the spread of influences amongst versatile populations. It corresponds to a non-standard urn with balls of two colours: each time a ball is drawn, it causes a ball of the other kind to switch its colour. The pr

Externí odkaz: https://doaj.org/article/f350d122af4949ae8ad777f055023e22

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Akademický článek

HyperLogLog: the analysis of a near-optimal cardinality estimation algorithm

Autor: Philippe Flajolet, Éric Fusy, Olivier Gandouet, Frédéric Meunier

Publikováno v: Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings vol. AH,..., Iss Proceedings (2007)

This extended abstract describes and analyses a near-optimal probabilistic algorithm, HYPERLOGLOG, dedicated to estimating the number of \emphdistinct elements (the cardinality) of very large data ensembles. Using an auxiliary memory of m units (typi

Externí odkaz: https://doaj.org/article/24b2d87559e0433c99d8b9d2f7018587

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Akademický článek

Some exactly solvable models of urn process theory

Autor: Philippe Flajolet, Philippe Dumas, Vincent Puyhaubert

Publikováno v: Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings vol. AG,..., Iss Proceedings (2006)

We establish a fundamental isomorphism between discrete-time balanced urn processes and certain ordinary differential systems, which are nonlinear, autonomous, and of a simple monomial form. As a consequence, all balanced urn processes with balls of

Externí odkaz: https://doaj.org/article/4e4bda94108c4e81897307653d93b203

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Elektronická kniha

Analytic Combinatorics

Autor: Philippe Flajolet, Robert Sedgewick

Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific mo

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Some New Self-avoiding Walk and Polygon Models

Autor: Philippe Flajolet, Anthony J. Guttmann, Nicholas R. Beaton, Timothy M. Garoni

Publikováno v: Fundamenta Informaticae. 117:19-33

We study the behaviour of prudent, perimeter and quasi-prudent self-avoiding walks and polygons in both two and three dimensions, as well as some solvable subsets. Our analysis combines exact solutions of some simpler cases, careful asymptotic analys

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::66faa841b0355a1939c114bae340526f
https://doi.org/10.3233/fi-2012-686

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The distribution of height and diameter in random non-plane binary trees

Autor: Nicolas Broutin, Philippe Flajolet

Publikováno v: Random Structures & Algorithms. 41:215-252

This study is dedicated to precise distributional analyses of the height of non-plane unlabelled binary trees ("Otter trees"), when trees of a given size are taken with equal likelihood. The height of a rooted tree of size $n$ is proved to admit a li

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::37e7d586f67d659d858e03f1cf9f8cf9
https://doi.org/10.1002/rsa.20393

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Pseudo-factorials, elliptic functions, and continued fractions

Autor: Roland Bacher, Philippe Flajolet

Publikováno v: Ramanujan Journal
Ramanujan Journal, Springer Verlag, 2010, 21 (1), pp.71-97. ⟨10.1007/s11139-009-9186-9⟩
Ramanujan Journal, 2010, 21 (1), pp.71-97. ⟨10.1007/s11139-009-9186-9⟩

This study presents miscellaneous properties of pseudo-factorials, which are numbers whose recurrence relation is a twisted form of that of usual factorials. These numbers are associated with special elliptic functions, most notably, a Dixonian and a

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::646c8dc87bd4fc0e2390a2b66ffac4da
https://doi.org/10.1007/s11139-009-9186-9

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