Skip to main content
SpringerLink
Log in

Minimal de Bruijn Sequence in a Language with Forbidden Substrings

  • Conference paper
Graph-Theoretic Concepts in Computer Science (WG 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3353))

Included in the following conference series:

Abstract

Let be the following strategy to construct a walk in a labeled digraph: at each vertex, we follow the unvisited arc of minimum label. In this work we study for which languages, applying the previous strategy over the corresponding de Bruijn graph, we finish with an Eulerian cycle, in order to obtain the minimal de Bruijn sequence of the language.

Partially supported by ECOS C00E03 (French-Chilean Cooperation), Programa Iniciativa Científica Milenio P01-005, and CONICYT Ph.D. Fellowship.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. de Bruijn, N.G.: A combinatorial problem. Nederl. Akad. Wetensch., Proc. 49, 758–764 (1946)

    MathSciNet  Google Scholar 

  2. Stein, S.K.: The mathematician as an explorer. Sci. Amer. 204, 148–158 (1961)

    Article  MathSciNet  Google Scholar 

  3. Bermond, J.C., Dawes, R.W., Ergincan, F.Ö.: De Bruijn and Kautz bus networks. Networks 30, 205–218 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  4. Chung, F., Diaconis, P., Graham, R.: Universal cycles for combinatorial structures. Discrete Math. 110, 43–59 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  5. Fredricksen, H.: A survey of full length nonlinear shift register cycle algorithms. SIAM Rev. 24, 195–221 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  6. Fredricksen, H., Maiorana, J.: Necklaces of beads in k colors and k-ary de Bruijn sequences. Discrete Math. 23, 207–210 (1978)

    MATH  MathSciNet  Google Scholar 

  7. Ruskey, F., Savage, C., Wang, T.M.: Generating necklaces. J. Algorithms 13, 414–430 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  8. Ruskey, F., Sawada, J.: Generating necklaces and strings with forbidden substrings. In: Du, D.-Z., Eades, P., Sharma, A.K., Lin, X., Estivill-Castro, V. (eds.) COCOON 2000. LNCS, vol. 1858, pp. 330–339. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  9. Moreno, E.: Lyndon words and de bruijn sequences in a subshift of finite type. In: Harju, T., Karhumäki, J. (eds.) Proceedings of WORDS 2003. TUCS General Publications, Turku, Finland, vol. 27, pp. 400–410. Turku Centre for Computer Science (2003)

    Google Scholar 

  10. Lind, D., Marcus, B.: Symbolic Dynamics and Codings. Cambridge University Press, Cambridge (1995)

    Book  Google Scholar 

  11. Tutte, W.T.: Graph theory. Encyclopedia of Mathematics and its Applications, vol. 21. Addison-Wesley Publishing Company Advanced Book Program, Reading (1984)

    MATH  Google Scholar 

  12. Matamala, M., Moreno, E.: Minimal Eulerian cycle in a labeled digraph. Technical Report CMM-B-04/08-108, DIM-CMM, Universidad de Chile (2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 170-3, Correo 3, Santiago, Chile

    Eduardo Moreno & Martín Matamala

  2. Centro de Modelamiento Matemático, UMR 2071, UCHILE-CNRS, Casilla 170-3, Correo 3, Santiago, Chile

    Martín Matamala

  3. Institut Gaspard Monge, Université de Marne-la-Vallée, Champs-sur-Marne, 77454, Marne-la-Vallée cedex 2, France

    Eduardo Moreno

Authors
  1. Eduardo Moreno
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Martín Matamala
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, ETH Zurich, ETH Zentrum, CH-8022, Zurich, Switzerland

    Juraj Hromkovič

  2. Department of Computer Science, RWTH Aachen, Chair of Computer Science III, Aachen, Germany

    Manfred Nagl

  3. Department of Computer Science III, RWTH Aachen University, Ahornstra{ß}e 55, 52074, Aachen, Germany

    Bernhard Westfechtel

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Moreno, E., Matamala, M. (2004). Minimal de Bruijn Sequence in a Language with Forbidden Substrings. In: Hromkovič, J., Nagl, M., Westfechtel, B. (eds) Graph-Theoretic Concepts in Computer Science. WG 2004. Lecture Notes in Computer Science, vol 3353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30559-0_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-30559-0_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24132-4

  • Online ISBN: 978-3-540-30559-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation