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Pré-Publication, Document De Travail Année : 2014

Random-bit optimal uniform sampling for rooted planar trees with given sequence of degrees and Applications

David Julien
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Résumé

In this paper, we redesign and simplify an algorithm due to Remy et al. for the generation of rooted planar trees that satisfies a given partition of degrees. This new version is now optimal in terms of random bit complexity, up to a multiplicative constant. We then apply a natural process ''simulate-guess-and-proof'' to analyze the height of a random Motzkin in function of its frequency of unary nodes. When the number of unary nodes dominates, we prove some unconventional height phenomenon (i.e. outside the universal square root behaviour.)
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Dates et versions

hal-00932993 , version 1 (19-01-2014)

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Olivier Bodini, David Julien, Marchal Philippe. Random-bit optimal uniform sampling for rooted planar trees with given sequence of degrees and Applications. 2014. ⟨hal-00932993⟩
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