# A repertoire for additive functionals of uniformly distributed m-ary search trees

Abstract : Using recent results on singularity analysis for Hadamard products of generating functions, we obtain the limiting distributions for additive functionals on $m$-ary search trees on $n$ keys with toll sequence $(i) n^α$ with $α ≥ 0 (α =0$ and $α =1$ correspond roughly to the space requirement and total path length, respectively); $(ii) ln \binom{n} {m-1}$, which corresponds to the so-called shape functional; and $(iii) $1$_{n=m-1}$, which corresponds to the number of leaves.
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Communication dans un congrès
Conrado Martínez. 2005 International Conference on Analysis of Algorithms, 2005, Barcelona, Spain. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms, pp.105-114, 2005, DMTCS Proceedings
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https://hal.inria.fr/hal-01184042
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Soumis le : mercredi 12 août 2015 - 15:52:39
Dernière modification le : mercredi 10 mai 2017 - 17:39:23
Document(s) archivé(s) le : vendredi 13 novembre 2015 - 11:40:49

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• HAL Id : hal-01184042, version 1

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James Allen Fill, Nevin Kapur. A repertoire for additive functionals of uniformly distributed m-ary search trees. Conrado Martínez. 2005 International Conference on Analysis of Algorithms, 2005, Barcelona, Spain. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms, pp.105-114, 2005, DMTCS Proceedings. 〈hal-01184042〉

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