Olivier Bodini ; Yann Ponty - Multi-dimensional Boltzmann Sampling of Languages

dmtcs:2793 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10) - https://doi.org/10.46298/dmtcs.2793
Multi-dimensional Boltzmann Sampling of LanguagesArticle

Authors: Olivier Bodini ORCID1; Yann Ponty ORCID2,3

  • 1 Algorithmes, Programmes et Résolution
  • 2 Algorithms and Models for Integrative Biology
  • 3 Laboratoire d'informatique de l'École polytechnique [Palaiseau]

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.


Volume: DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: Random generation,Boltzmann sampling,Context-free languages,[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG]

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