Multi-dimensional Boltzmann Sampling of Languages

Olivier Bodini 1 Yann Ponty 2, 3
1 APR - Algorithmes, Programmes et Résolution
LIP6 - Laboratoire d'Informatique de Paris 6
2 AMIB - Algorithms and Models for Integrative Biology
CNRS - Centre National de la Recherche Scientifique : UMR8623, Polytechnique - X, Inria Saclay - Ile de France, UP11 - Université Paris-Sud - Paris 11, LRI - Laboratoire de Recherche en Informatique, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
Abstract : We address the uniform random generation of words from a context-free language (over an alphabet of size $k$), while constraining every letter to a targeted frequency of occurrence. Our approach consists in a multidimensional extension of Boltzmann samplers. We show that, under mostly $\textit{strong-connectivity}$ hypotheses, our samplers return a word of size in $[(1- \epsilon)n, (1+ \epsilon)n]$ and exact frequency in $\mathcal{O}(n^{1+k/2})$ expected time. Moreover, if we accept tolerance intervals of width in $\Omega (\sqrt{n})$ for the number of occurrences of each letters, our samplers perform an approximate-size generation of words in expected $\mathcal{O}(n)$ time. We illustrate our approach on the generation of Tetris tessellations with uniform statistics in the different types of tetraminoes.
Type de document :
Communication dans un congrès
Drmota, Michael and Gittenberger, Bernhard. 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), Jun 2010, Vienna, Austria. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), pp.49-64, 2010, DMTCS Proceedings
Liste complète des métadonnées

Littérature citée [14 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-00450763
Contributeur : Coordination Episciences Iam <>
Soumis le : jeudi 20 août 2015 - 16:33:34
Dernière modification le : jeudi 11 janvier 2018 - 06:26:46
Document(s) archivé(s) le : mercredi 26 avril 2017 - 10:09:36

Fichier

dmAM0104.pdf
Fichiers éditeurs autorisés sur une archive ouverte

Identifiants

  • HAL Id : hal-00450763, version 4

Citation

Olivier Bodini, Yann Ponty. Multi-dimensional Boltzmann Sampling of Languages. Drmota, Michael and Gittenberger, Bernhard. 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), Jun 2010, Vienna, Austria. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), pp.49-64, 2010, DMTCS Proceedings. 〈hal-00450763v4〉

Partager

Métriques

Consultations de la notice

247

Téléchargements de fichiers

763