Skip to main content
SpringerLink
Log in
Book cover

Structures in Logic and Computer Science pp 192–211Cite as

On compact directed acyclic word graphs

  • Pattern Matching and Learning
  • Chapter
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1261))

Abstract

The Directed Acyclic Word Graph (DAWG) is a space-efficient data structure to treat and analyze repetitions in a text, especially in DNA genomic sequences. Here, we consider the Compact Directed Acyclic Word Graph of a word. We give the first direct algorithm to construct it. It runs in time linear in the length of the string on a fixed alphabet. Our implementation requires half the memory space used by DAWGs.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Apostolico. The myriad virtues of subword trees. In A. Apostolico & Z. Galil, editor, Combinatorial Algorithms on Words., pages 85–95. Springer-Verlag, 1985.

    Google Scholar 

  2. A. Blumer, J. Blumer, A. Ehrenfeucht, D. Haussler, and R. McConnel. Linear size finite automata for the set of all subwords of a word: an outline of results. Bull. European Assoc. Theoret. Comput. Sci., 21:12–20, 1983.

    Google Scholar 

  3. A. Blumer, J. Blumer, D. Haussler, A. Ehrenfeucht, M.T. Chen, and J. Seiferas. The smallest automaton recognizing the subwords of a text. Theoret. Comput. Sci., 40:31–55, 1985.

    Google Scholar 

  4. A. Blumer, J. Blumer, D. Haussler, and R. McConnell. Complete inverted files for efficient text retrieval and analysis. Journal of the Association for Computing Machinery, 34(3):578–595, July 1987.

    Google Scholar 

  5. A. Blumer, D. Haussler, and A. Ehrenfeucht. Average sizes of suffix trees and dawgs. Discrete Applied Mathematics, 24:37–45, 1989.

    Google Scholar 

  6. B. Clift, D. Haussler, R. McDonnell, T.D. Schneider, and G.D. Stormo. Sequence landscapes. Nucleic Acids Research, 4(1):141–158, 1986.

    Google Scholar 

  7. M. Crochemore. Recherche linéaire d'un carré dans un mot. C. R. Acad. Sci. Paris Sér. I Math., 296:781–784, 1983.

    Google Scholar 

  8. M. Crochemore. Optimal factor tranducers. In A. Apostolico and Z. Galil, editors, Combinatorial Algorithms on Words, volume 12 of NATO Advanced Science Institutes, Series F, pages 31–44. Springer-Verlag, Berlin, 1985.

    Google Scholar 

  9. M. Crochemore. Transducers and repetitions. Theoret. Comput. Sci., 45(1):63–86, 1986.

    Google Scholar 

  10. M. Crochemore. Longest common factor of two words. In H. Ehrig, R. Kowalski, G. Levi, and U. Montanari, editors, TAPSOFT, number 249 in Lecture Notes in Computer Science, pages 26–36. Springer-Verlag, Berlin, 1987.

    Google Scholar 

  11. M. Crochemore and C. Hancart. Automata for matching patterns. In G. Rozenberg and A. Salomaa, editors, Handbook of Formal Languages. Springer-Verlag, 1997. to appear.

    Google Scholar 

  12. M. Crochemore and W. Rytter. Text Algorithms, chapter 5–6, pages 73–130. Oxford University Press, New York, 1994.

    Google Scholar 

  13. M. Farach. Optimal suffix tree construction with large alphabets. manuscript, October 1996.

    Google Scholar 

  14. R. W. Irving. Suffix binary search trees. Technical report TR-1995-7, Computing Science Department, University of Glasgow, April 1995.

    Google Scholar 

  15. J. Karkkainen. Suffix cactus: a cross between suffix tree and suffix array. Combinatorial Pattern Matching, 937:191–204, July 1995.

    Google Scholar 

  16. C. Lefevre and J-E. Ikeda. The position end-set tree: A small automaton for word recognition in biological sequences. CABIOS, 9(3):343–348, 1993.

    Google Scholar 

  17. U. Manber and G. Myers. Suffix arrays: A new method for on-line string searches. SIAM J. Comput., 22(5):935–948, Oct. 1993.

    Google Scholar 

  18. E. McCreight. A space-economical suffix tree construction algorithm. Journal of the ACM, 23(2):262–272, Apr. 1976.

    Google Scholar 

  19. G. A. Stephen. String searching algorithms. World Scientific Press, 1994.

    Google Scholar 

  20. E. Ukkonen. On-line construction of suffix trees. Algorithmica, 14:249–260, 1995.

    Google Scholar 

  21. E. Ukkonen and D. Wood. Approximate string matching with suffix automata. Algorithmica, 10(5):353–364, 1993.

    Google Scholar 

  22. P. Weiner. Linear pattern matching algorithm. In 14th Annual IEEE Symposium on Switching and Automata Theory, pages 1–11, Washington, DC, 1973.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut Gaspard Monge, Université de Marne-La-Vallée, 2, rue de la Butte Verte, F-93160, Noisy-Le-Grand

    Maxime Crochemore & Renaud Vérin

Authors
  1. Maxime Crochemore
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Renaud Vérin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Jan Mycielski Grzegorz Rozenberg Arto Salomaa

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Crochemore, M., Vérin, R. (1997). On compact directed acyclic word graphs. In: Mycielski, J., Rozenberg, G., Salomaa, A. (eds) Structures in Logic and Computer Science. Lecture Notes in Computer Science, vol 1261. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63246-8_12

Download citation

  • DOI: https://doi.org/10.1007/3-540-63246-8_12

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63246-7

  • Online ISBN: 978-3-540-69242-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation