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Succinct Representations of Ordinal Trees

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Space-Efficient Data Structures, Streams, and Algorithms

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8066))

Abstract

We survey succinct representations of ordinal, or rooted, ordered trees. Succinct representations use space that is close to the appropriate information-theoretic minimum, but support operations on the tree rapidly, usually in O(1) time.

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References

  1. Aho, A.V., Hopcroft, J.E., Ullman, J.D.: On finding lowest common ancestors in trees. In: Aho, A.V., Borodin, A., Constable, R.L., Floyd, R.W., Harrison, M.A., Karp, R.M., Strong, H.R. (eds.) STOC, pp. 253–265. ACM (1973)

    Google Scholar 

  2. Arroyuelo, D., Cánovas, R., Navarro, G., Sadakane, K.: Succinct trees in practice. In: Blelloch, G.E., Halperin, D. (eds.) ALENEX, pp. 84–97. SIAM (2010)

    Google Scholar 

  3. Arroyuelo, D., Claude, F., Maneth, S., Mäkinen, V., Navarro, G., Nguyen, K., Sirén, J., Välimäki, N.: Fast in-memory XPath search using compressed indexes. In: Li, F., Moro, M.M., Ghandeharizadeh, S., Haritsa, J.R., Weikum, G., Carey, M.J., Casati, F., Chang, E.Y., Manolescu, I., Mehrotra, S., Dayal, U., Tsotras, V.J. (eds.) ICDE, pp. 417–428. IEEE (2010)

    Google Scholar 

  4. Barbay, J., He, M., Munro, J.I., Satti, S.R.: Succinct indexes for strings, binary relations and multilabeled trees. ACM Transactions on Algorithms 7(4), 52 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Benoit, D., Demaine, E.D., Munro, J.I., Raman, R., Raman, V., Rao, S.S.: Representing trees of higher degree. Algorithmica 43(4), 275–292 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. Berkman, O., Vishkin, U.: Finding level-ancestors in trees. J. Comput. Syst. Sci. 48(2), 214–230 (1994)

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  8. Chiang, Y.T., Lin, C.C., Lu, H.I.: Orderly spanning trees with applications. SIAM J. Comput. 34(4), 924–945 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. Chupa, K.: Efficient Representation of Binary Search Trees. Master’s thesis, University of Waterloo (1997)

    Google Scholar 

  10. Clark, D.R., Munro, J.I.: Efficient suffix trees on secondary storage (extended abstract). In: ACM-SIAM SODA, pp. 383–391 (1996)

    Google Scholar 

  11. Clark, D.R.: Compact PAT trees. Ph.D. thesis, University of Waterloo, Waterloo, Ontario., Canada (1998)

    Google Scholar 

  12. Darragh, J.J., Cleary, J.G., Witten, I.H.: Bonsai: a compact representation of trees. Softw. Pract. Exper. 23(3), 277–291 (1993)

    Article  Google Scholar 

  13. Delpratt, O., Raman, R., Rahman, N.: Engineering succinct DOM. In: EDBT. ACM Intl. Conference Proceeding Series, vol. 261, pp. 49–60. ACM (2008)

    Google Scholar 

  14. Delpratt, O., Rahman, N., Raman, R.: Engineering the LOUDS succinct tree representation. In: Àlvarez, C., Serna, M. (eds.) WEA 2006. LNCS, vol. 4007, pp. 134–145. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  15. Farzan, A., Munro, J.I.: A uniform approach towards succinct representation of trees. In: Gudmundsson, J. (ed.) SWAT 2008. LNCS, vol. 5124, pp. 173–184. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  16. Farzan, A., Munro, J.I.: Succinct representation of dynamic trees. Theor. Comput. Sci. 412(24), 2668–2678 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. Farzan, A., Raman, R., Rao, S.S.: Universal succinct representations of trees? In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009, Part I. LNCS, vol. 5555, pp. 451–462. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

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

    Google Scholar 

  19. Gál, A., Miltersen, P.B.: The cell probe complexity of succinct data structures. Theor. Comput. Sci. 379(3), 405–417 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  20. Geary, R.F., Raman, R., Raman, V.: Succinct ordinal trees with level-ancestor queries. ACM Transactions on Algorithms 2(4), 510–534 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  21. Geary, R.F., Rahman, N., Raman, R., Raman, V.: A simple optimal representation for balanced parentheses. Theor. Comput. Sci. 368(3), 231–246 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  22. Gog, S.: Succinct data structure library, SDSL (2013), https://github.com/simongog/sdsl

  23. Golin, M.J., Iacono, J., Krizanc, D., Raman, R., Rao, S.S., Shende, S.: Encoding 2-d range maximum queries. CoRR abs/1109.2885v2 (2012)

    Google Scholar 

  24. Golynski, A., Grossi, R., Gupta, A., Raman, R., Rao, S.S.: On the size of succinct indices. In: Arge, L., Hoffmann, M., Welzl, E. (eds.) ESA 2007. LNCS, vol. 4698, pp. 371–382. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  25. He, M., Munro, J.I., Rao, S.S.: Succinct ordinal trees based on tree covering. ACM Transactions on Algorithms 8(4), 42 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  26. Jacobson, G.J.: Space-efficient static trees and graphs. In: IEEE Symposium on Foundations of Computer Science, pp. 549–554 (1989)

    Google Scholar 

  27. Jansson, J., Sadakane, K., Sung, W.K.: Ultra-succinct representation of ordered trees with applications. Journal of Computer and System Sciences 78(2), 619–631 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  28. Joannou, S., Raman, R.: Dynamizing succinct tree representations. In: Klasing, R. (ed.) SEA 2012. LNCS, vol. 7276, pp. 224–235. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  29. Jurkiewicz, T., Mehlhorn, K.: The cost of address translation. In: Sanders, P., Zeh, N. (eds.) ALENEX, pp. 148–162. SIAM (2010)

    Google Scholar 

  30. Katajainen, J., Mäkinen, E.: Tree compression and optimization with applications. Int. J. Found. Comput. Sci. 1(4), 425–448 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  31. Kurtz, S.: Reducing the space requirement of suffix trees. Softw., Pract. Exper. 29(13), 1149–1171 (1999)

    Article  Google Scholar 

  32. Lu, H., Yeh, C.: Balanced parentheses strike back. ACM Trans. Algorithms 4(3), 1–13 (2008)

    Article  MathSciNet  Google Scholar 

  33. 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 

  34. Munro, J.I., Raman, V., Rao, S.S.: Space efficient suffix trees. J. Algorithms 39(2), 205–222 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  35. Munro, J.I., Raman, V., Storm, A.J.: Representing dynamic binary trees succinctly. In: Kosaraju, S.R. (ed.) SODA, pp. 529–536. ACM/SIAM (2001)

    Google Scholar 

  36. Munro, J.I., Rao, S.S.: Succinct representations of functions. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 1006–1015. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  37. Ottaviano, G.: The succinct library (2013), https://github.com/ot/succinct

  38. Grossi, R., Ottaviano, G.: Design of practical succinct data structures for large data collections. In: Bonifaci, V., Demetrescu, C., Marchetti-Spaccamela, A. (eds.) SEA 2013. LNCS, vol. 7933, pp. 5–17. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  39. Patrascu, M.: Succincter. In: FOCS, pp. 305–313. IEEE Computer Society (2008)

    Google Scholar 

  40. Poyias, A.: XXML: Handling extra-large XML documents. siXML technology whitepaper (February 2013), https://lra.le.ac.uk/bitstream/2381/27744/1/SiXDOMWhitepaper.pdf

  41. Raman, R., Raman, V., Rao, S.S.: Succinct indexable dictionaries with applications to encoding k-ary trees, prefix sums and multisets. ACM Transactions on Algorithms 3(4), 43 (2007); Preliminary version in SODA 2002

    Article  MathSciNet  MATH  Google Scholar 

  42. Raman, R., Rao, S.S.: Succinct dynamic dictionaries and trees. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 357–368. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  43. Sadakane, K., Navarro, G.: Fully-functional succinct trees. In: Charikar, M. (ed.) SODA, pp. 134–149. SIAM (2010)

    Google Scholar 

  44. Sleator, D.D., Tarjan, R.E.: Self-adjusting binary search trees. J. ACM 32(3), 652–686 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  45. Tabei, Y.: Succinct multibit tree: Compact representation of multibit trees by using succinct data structures in chemical fingerprint searches. In: Raphael, B., Tang, J. (eds.) WABI 2012. LNCS, vol. 7534, pp. 201–213. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

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

    Rajeev Raman

  2. School of Computer Science and Engineering, Seoul National University, South Korea

    S. Srinivasa Rao

Authors
  1. Rajeev Raman
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  2. S. Srinivasa Rao
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Editor information

Editors and Affiliations

  1. Faculty of Computer and Information Science, University of Ljubljana, Ljubljana, Slovenia

    Andrej Brodnik

  2. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, Canada

    Alejandro López-Ortiz

  3. The Institute of Mathematical Sciences, Chennai, India

    Venkatesh Raman

  4. Facultad de Ingeniería, Universidad de la República, Montevideo, Uruguay

    Alfredo Viola

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Raman, R., Rao, S.S. (2013). Succinct Representations of Ordinal Trees. In: Brodnik, A., López-Ortiz, A., Raman, V., Viola, A. (eds) Space-Efficient Data Structures, Streams, and Algorithms. Lecture Notes in Computer Science, vol 8066. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40273-9_20

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  • DOI: https://doi.org/10.1007/978-3-642-40273-9_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40272-2

  • Online ISBN: 978-3-642-40273-9

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