Skip to main content
SpringerLink
Log in

Tree Compression with Top Trees

  • 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 introduce a new compression scheme for labeled trees based on top trees [3]. Our compression scheme is the first to simultaneously take advantage of internal repeats in the tree (as opposed to the classical DAG compression that only exploits rooted subtree repeats) while also supporting fast navigational queries directly on the compressed representation. We show that the new compression scheme achieves close to optimal worst-case compression, can compress exponentially better than DAG compression, is never much worse than DAG compression, and supports navigational queries in logarithmic time.

A draft of the full version of the paper can be found as Arxiv preprint arXiv:1304.5702.

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. Adiego, J., Navarro, G., de la Fuente, P.: Lempel-Ziv compression of highly structured documents. J. Amer. Soc. Inf. Sci. and Techn. 58(4), 461–478 (2007)

    Article  Google Scholar 

  2. Alstrup, S., Holm, J., de Lichtenberg, K., Thorup, M.: Minimizing diameters of dynamic trees. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds.) ICALP 1997. LNCS, vol. 1256, pp. 270–280. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  3. Alstrup, S., Holm, J., Lichtenberg, K.D., Thorup, M.: Maintaining information in fully-dynamic trees with top trees. ACM Trans. Algorithms 1, 243–264 (2003)

    Article  Google Scholar 

  4. Alstrup, S., Holm, J., Thorup, M.: Maintaining center and median in dynamic trees. In: Halldórsson, M.M. (ed.) SWAT 2000. LNCS, vol. 1851, pp. 46–56. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  5. Benoit, D., Demaine, E., Munro, I., Raman, R., Raman, V., Rao, S.: Representing trees of higher degree. Algorithmica 43, 275–292 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bille, P., Gørtz, I.L., Landau, G.M., Weimann, O.: Tree compression with top trees. Arxiv preprint arXiv:1304.5702 (2013)

    Google Scholar 

  7. Bille, P., Landau, G., Raman, R., Rao, S., Sadakane, K., Weimann, O.: Random access to grammar-compressed strings. In: Proc. 22nd SODA, pp. 373–389 (2011)

    Google Scholar 

  8. Buneman, P., Grohe, M., Koch, C.: Path queries on compressed XML. In: Proc. 29th VLDB, pp. 141–152 (2003)

    Google Scholar 

  9. Busatto, G., Lohrey, M., Maneth, S.: Grammar-based tree compression. Technical report, EPFL (2004)

    Google Scholar 

  10. Busatto, G., Lohrey, M., Maneth, S.: Efficient memory representation of XML document trees. Information Systems 33(4-5), 456–474 (2008)

    Article  Google Scholar 

  11. Charikar, M., Lehman, E., Lehman, A., Liu, D., Panigrahy, R., Prabhakaran, M., Sahai, A., Shelat, A.: The smallest grammar problem. IEEE Trans. Inform. Theory 51(7), 2554–2576 (2005)

    Article  MathSciNet  Google Scholar 

  12. Downey, P.J., Sethi, R., Tarjan, R.E.: Variations on the common subexpression problem. J. ACM 27, 758–771 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  13. Ferragina, P., Luccio, F., Manzini, G., Muthukrishnan, S.: Compressing and indexing labeled trees, with applications. J. ACM 57, 1–33 (2009)

    Article  MathSciNet  Google Scholar 

  14. Frick, M., Grohe, M., Koch, C.: Query evaluation on compressed trees. In: Proc. 18th LICS, pp. 188–197 (2003)

    Google Scholar 

  15. Geary, R., Raman, R., Raman, V.: Succinct ordinal trees with level-ancestor queries. In: Proc. 15th SODA, pp. 1–10 (2004)

    Google Scholar 

  16. Jacobson, G.: Space-efficient static trees and graphs. In: Proc. 30th FOCS, pp. 549–554 (1989)

    Google Scholar 

  17. Lohrey, M., Maneth, S.: The complexity of tree automata and XPath on grammar-compressed trees. Theoret. Comput. Sci. 363(2) (2006)

    Google Scholar 

  18. Lohrey, M., Maneth, S., Mennicke, R.: Tree structure compression with repair. Arxiv preprint arXiv:1007.5406 (2010)

    Google Scholar 

  19. Maneth, S., Busatto, G.: Tree transducers and tree compressions. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 363–377. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  20. Munro, J.I., Raman, V.: Succinct representation of balanced parentheses and static trees. SIAM J. Comput. 31(3), 762–776 (2001)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. DTU Compute, Technical University of Denmark, Denmark

    Philip Bille & Inge Li Gørtz

  2. University of Haifa, Israel

    Gad M. Landau & Oren Weimann

Authors
  1. Philip Bille
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Inge Li Gørtz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gad M. Landau
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Oren Weimann
    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

Bille, P., Gørtz, I.L., Landau, G.M., Weimann, O. (2013). Tree Compression with Top Trees. 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_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-39206-1_14

  • 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

Search

Navigation