Skip to main content
Springer Nature Link
Log in

Dynamic Compressed Strings with Random Access

  • Conference paper
Automata, Languages, and Programming (ICALP 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7965))

Included in the following conference series:

Abstract

We consider the problem of storing a string S in dynamic compressed form, while permitting operations directly on the compressed representation of S: access a substring of S; replace, insert or delete a symbol in S; count how many occurrences of a given symbol appear in any given prefix of S (called rank operation) and locate the position of the ith occurrence of a symbol inside S (called select operation). We discuss the time complexity of several combinations of these operations along with the entropy space bounds of the corresponding compressed indexes. In this way, we extend or improve the bounds of previous work by Ferragina and Venturini [TCS, 2007], Jansson et al. [ICALP, 2012], and Nekrich and Navarro [SODA, 2013].

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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.

Similar content being viewed by others

References

  1. Barbay, J., He, M., Munro, J.I., Satti, S.R.: Succinct indexes for strings, binary relations and multilabeled trees. ACM Transactions on Algorithms 7, 52 (2011)

    Article  MathSciNet  Google Scholar 

  2. Brodnik, A., Carlsson, S., Demaine, E.D., Munro, J.I., Sedgewick, R.: Resizable arrays in optimal time and space. In: Dehne, F., Gupta, A., Sack, J.-R., Tamassia, R. (eds.) WADS 1999. LNCS, vol. 1663, pp. 37–48. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  3. Dietzfelbinger, M., Karlin, A.R., Mehlhorn, K., Meyer auf der Heide, F., Rohnert, H., Tarjan, R.E.: Dynamic perfect hashing: Upper and lower bounds. SIAM J. Comput. 23, 738–761 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ferragina, P., Luccio, F., Manzini, G., Muthukrishnan, S.: Compressing and indexing labeled trees, with applications. J. ACM 57 (2009)

    Google Scholar 

  5. Ferragina, P., Manzini, G.: Indexing compressed text. J. ACM 52, 552–581 (2005)

    Article  MathSciNet  Google Scholar 

  6. Ferragina, P., Venturini, R.: A simple storage scheme for strings achieving entropy bounds. Theor. Comput. Sci. 372, 115–121 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  7. Fredman, M.L., Saks, M.E.: The cell probe complexity of dynamic data structures. In: STOC, pp. 345–354 (1989)

    Google Scholar 

  8. González, R., Navarro, G.: Compressed text indexes with fast locate. In: Ma, B., Zhang, K. (eds.) CPM 2007. LNCS, vol. 4580, pp. 216–227. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  9. Grossi, R., Orlandi, A., Raman, R.: Optimal trade-offs for succinct string indexes. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010, Part I. LNCS, vol. 6198, pp. 678–689. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  10. Grossi, R., Vitter, J.S.: Compressed suffix arrays and suffix trees with applications to text indexing and string matching. SIAM J. Computing 35, 378–407 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. Jansson, J., Sadakane, K., Sung, W.-K.: CRAM: Compressed random access memory. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012, Part I. LNCS, vol. 7391, pp. 510–521. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  12. Manzini, G.: An analysis of the Burrows-Wheeler transform. J. ACM 48, 407–430 (2001)

    Article  MathSciNet  Google Scholar 

  13. Navarro, G., Nekrich, Y.: Optimal dynamic sequence representations. In: Proc. 24th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA (2013)

    Google Scholar 

  14. Pagh, R.: A new trade-off for deterministic dictionaries. In: Halldórsson, M.M. (ed.) SWAT 2000. LNCS, vol. 1851, pp. 22–31. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  15. Pagh, R., Rodler, F.F.: Cuckoo hashing. J. Algorithms 51, 122–144 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  16. Pǎtraşcu, M., Demaine, E.D.: Logarithmic lower bounds in the cell-probe model. SIAM J. Comput. 35, 932–963 (2006)

    Article  MathSciNet  Google Scholar 

  17. Patrascu, M., Viola, E.: Cell-probe lower bounds for succinct partial sums. In: Charikar, M. (ed.) SODA, pp. 117–122. SIAM (2010)

    Google Scholar 

  18. Raman, R., Raman, V., Rao, S.S.: Succinct indexable dictionaries with applications to encoding k-ary trees, prefix sums and multisets. ACM TALG 3 (2007)

    Google Scholar 

  19. Raman, R., Raman, V., Rao, S.S.: Succinct Dynamic Data Structures. In: Dehne, F., Sack, J.-R., Tamassia, R. (eds.) WADS 2001. LNCS, vol. 2125, pp. 426–437. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  20. Sadakane, K., Grossi, R.: Squeezing succinct data structures into entropy bounds. In: SODA, pp. 1230–1239. ACM Press (2006)

    Google Scholar 

  21. Sadakane, K., Navarro, G.: Fully-functional succinct trees. In: SODA, pp. 134–149 (2010)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Università di Pisa, Italy

    Roberto Grossi & Rossano Venturini

  2. Department of Computer Science, University of Leicester, UK

    Rajeev Raman

  3. School of Computer Science and Engineering, Seoul National Univerity, Korea

    Satti Srinivasa Rao

Authors
  1. Roberto Grossi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rajeev Raman
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Satti Srinivasa Rao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Rossano Venturini
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, Postboks 7803, 5020, Bergen, Norway

    Fedor V. Fomin

  2. Faculty of Computing, University of Latvia, Raina bulv. 19, 1586, Riga, Latvia

    Rūsiņš Freivalds

  3. Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Marta Kwiatkowska

  4. Faculty of Mathematics and Computer Science, Weizmann Institute of Science, POB 26, 76100, Rehovot, Israel

    David Peleg

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Grossi, R., Raman, R., Rao, S.S., Venturini, R. (2013). Dynamic Compressed Strings with Random Access. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds) Automata, Languages, and Programming. ICALP 2013. Lecture Notes in Computer Science, vol 7965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39206-1_43

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-39206-1_43

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39205-4

  • Online ISBN: 978-3-642-39206-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics