Skip to main content

Random Sampling from Boltzmann Principles

  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2380))

Included in the following conference series:

Abstract

This extended abstract proposes a surprisingly simple framework for the random generation of combinatorial configurations based on Boltzmann models. Random generation of possibly complex structured objects is performed by placing an appropriate measure spread over the whole of a combinatorial class. The resulting algorithms can be implemented easily within a computer algebra system, be analysed mathematically with great precision, and, when suitably tuned, tend to be efficient in practice, as they often operate in linear time.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barcucci, E., Pinzani, R., AND Sprugnoli, R. The random generation of directed animals. Theoretical Computer Science 127, 2 (1994), 333–350.

    Article  MATH  MathSciNet  Google Scholar 

  2. Bergeron, F., Labelle, G., AND Leroux, P. Combinatorial species and treelike structures. Cambridge University Press, Cambridge, 1998. Translated from the 1994 French original by Margaret Readdy, With a foreword by Gian-Carlo Rota.

    Google Scholar 

  3. Denise, A., AND Zimmermann, P. Uniform random generation of decomposable structures using floating-point arithmetic. Theoretical Computer Science 218, 2 (1999), 233–248.

    Article  MATH  MathSciNet  Google Scholar 

  4. Devroye, L. Non-Uniform Random Variate Generation. Springer Verlag, 1986.

    Google Scholar 

  5. Duchon, P., Flajolet, P., Louchard, G., AND Schaeffer, G. Boltzmann samplers for random combinatorial generation. In preparation, 2002.

    Google Scholar 

  6. Flajolet, P., Salvy, B., AND Zimmermann, P. Automatic average-case analysis of algorithms. Theoretical Computer Science 79, 1 (Feb. 1991), 37–109.

    Article  MATH  MathSciNet  Google Scholar 

  7. Flajolet, P., AND Sedgewick, R. Analytic Combinatorics. 2001. Book in preparation: Individual chapters are available as INRIA Research Reports 1888, 2026, 2376, 2956, 3162, 4103 and electronically under http://algo.inria.fr/flajolet/Publications/books.html.

  8. Flajolet, P., Zimmermann, P., AND Van Cutsem, B. A calculus for the random generation of labelled combinatorial structures. Theoretical Computer Science 132, 1–2 (1994), 1–35.

    Article  MATH  MathSciNet  Google Scholar 

  9. Goulden, I. P., AND Jackson, D. M. Combinatorial Enumeration. John Wiley, New York, 1983.

    MATH  Google Scholar 

  10. Knuth, D. E., AND Yao, A. C. The complexity of nonuniform random number generation. In Algorithms and complexity (Proc. Sympos., Carnegie-Mellon Univ., Pittsburgh, Pa., 1976). Academic Press, New York, 1976, pp. 357–428.

    Google Scholar 

  11. Louchard, G. Asymptotic properties of some underdiagonal walks generation algorithms. Theoretical Computer Science 218, 2 (1999), 249–262.

    Article  MATH  MathSciNet  Google Scholar 

  12. Nijenhuis, A., AND Wilf, H. S. Combinatorial Algorithms, second ed. Academic Press, 1978.

    Google Scholar 

  13. Odlyzko, A. M. Asymptotic enumeration methods. In Handbook of Combinatorics, R. Graham, M. Grötschel, and L. Lovász, Eds., vol. II. Elsevier, Amsterdam, 1995, pp. 1063–1229.

    Google Scholar 

  14. Sloane, N. J. A. The On-Line Encyclopedia of Integer Sequences. 2000. Published electronically at http://www.research.att.com/~njas/sequences/.

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Duchon, P., Flajolet, P., Louchard, G., Schaeffer, G. (2002). Random Sampling from Boltzmann Principles. In: Widmayer, P., Eidenbenz, S., Triguero, F., Morales, R., Conejo, R., Hennessy, M. (eds) Automata, Languages and Programming. ICALP 2002. Lecture Notes in Computer Science, vol 2380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45465-9_43

Download citation

  • DOI: https://doi.org/10.1007/3-540-45465-9_43

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43864-9

  • Online ISBN: 978-3-540-45465-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics