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

Abstract : 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 limiting theta distribution, both in a central and local sense, as well as obey moderate as well as large deviations estimates. The approximations obtained for height also yield the limiting distribution of the diameter of unrooted trees. The proofs rely on a precise analysis, in the complex plane and near singularities, of generating functions associated with trees of bounded height.
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Article dans une revue
Random Structures and Algorithms, Wiley, 2011, 41 (2), pp.215-252. 〈10.1002/rsa.20393〉
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https://hal.inria.fr/hal-00773369
Contributeur : Nicolas Broutin <>
Soumis le : dimanche 13 janvier 2013 - 16:08:44
Dernière modification le : mercredi 29 novembre 2017 - 15:11:15

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Nicolas Broutin, Philippe Flajolet. The distribution of height and diameter in random non-plane binary trees. Random Structures and Algorithms, Wiley, 2011, 41 (2), pp.215-252. 〈10.1002/rsa.20393〉. 〈hal-00773369〉

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