Analytic samplers and the combinatorial rejection method

Olivier Bodini, Jeremie Lumbroso, Nicolas Rolin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Abstract

Boltzmann samplers, introduced by Duchon et al. in 2001, make it possible to uniformly draw approximate size objects from any class which can be specified through the symbolic method. This, through by evaluating the associated generating functions to obtain the correct branching probabilities. But these samplers require generating functions, in particular in the neighborhood of their sunglarity, which is a complex problem; they also require picking an appropriate tuning value to best control the size of generated objects. Although Pivoteau et al. have brought a sweeping question to the first question, with the introduction of their Newton oracle, questions remain. By adapting the rejection method, a classical tool from the random, we show how to obtain a variant of the Boltzmann sampler framework, which is tolerant of approximation, even large ones. Our goal for this is twofold: this allows for exact sampling with approximate values; but this also allows much more flexibility in tuning samplers. For the class of simple trees, we will show how this could be used to more easily calibrate samplers.

Original languageEnglish (US)
Title of host publication12th Workshop on Analytic Algorithmics and Combinatorics 2015, ANALCO 2015
PublisherSociety for Industrial and Applied Mathematics Publications
Pages40-50
Number of pages11
ISBN (Electronic)9781634398930
StatePublished - Jan 1 2015
Event12th Workshop on Analytic Algorithmics and Combinatorics, ANALCO 2015 - San Diego, United States
Duration: Jan 4 2015 → …

Publication series

Name12th Workshop on Analytic Algorithmics and Combinatorics 2015, ANALCO 2015

Conference

Conference12th Workshop on Analytic Algorithmics and Combinatorics, ANALCO 2015
CountryUnited States
CitySan Diego
Period1/4/15 → …

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Materials Chemistry
  • Discrete Mathematics and Combinatorics

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  • Cite this

    Bodini, O., Lumbroso, J., & Rolin, N. (2015). Analytic samplers and the combinatorial rejection method. In 12th Workshop on Analytic Algorithmics and Combinatorics 2015, ANALCO 2015 (pp. 40-50). (12th Workshop on Analytic Algorithmics and Combinatorics 2015, ANALCO 2015). Society for Industrial and Applied Mathematics Publications.