Efficient Implementation of Rank and Select Functions for Succinct Representation

  • Dong Kyue Kim
  • Joong Chae Na
  • Ji Eun Kim
  • Kunsoo Park
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3503)


Succinct representation is a space-efficient method to represent n discrete objects by O(n) bits. In order to access directly the ith object of succinctly represented data structures in constant time, two fundamental functions, rank and select are commonly used. However, little efforts were made on analyzing practical behaviors of these functions despite their importance for succinct representations.

In this paper we analyze the behavior of Clark’s algorithm which is the only one to support select in constant time using o(n)-bit space of extra space, and show that the performance of Clark’s algorithm gets worse as the number of 1’s in a bit-string becomes fewer and there exists a worst case in which a large amount of operations are needed. Then, we propose two algorithms that overcome the drawbacks of Clark’s. These algorithms take constant time forselect, and one uses o(n) bits for extra space and the other uses n + o(n) bits in the worst case. Experimental results show that our algorithms compute select faster than Clark’s.


Retrieval Time Block Number Extra Space Discrete Object Select Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Clark, D.R.: Compact Pat Trees. PhD thesis, University of Waterloo, Waterloo (1988)Google Scholar
  2. 2.
    Ferragina, P., Manzini, G.: Opportunistic data structures with applications. In: FOCS 2000, pp. 390–398 (2000)Google Scholar
  3. 3.
    Ferragina, P., Manzini, G.: An experimental study of an opportunistic index. In: SODA 2001, pp. 269–278 (2001)Google Scholar
  4. 4.
    Grossi, R., Gupta, A., Vitter, J.S.: High-order entropy-compressed text indexes. In: SODA 2003, pp. 841–850 (2003)Google Scholar
  5. 5.
    Grossi, R., Vitter, J.S.: Compressed suffix arrays and suffix trees with applications to text indexing and string matching. In: STOC 2000, pp. 397–406 (2000)Google Scholar
  6. 6.
    Hon, W.K., Sadakane, K., Sung, W.K.: Breaking a time-and-space barrier in constructing full-text indices. In: FOCS 2003, pp. 251–260 (2003)Google Scholar
  7. 7.
    Jacobson, G.: Succinct Static Data Structures. PhD thesis, Carnegie Mellon University, Pittsburgh (1988)Google Scholar
  8. 8.
    Jacobson, G.: Space-efficient static trees and graphs. In: FOCS 1989, pp. 549–554 (1989)Google Scholar
  9. 9.
    Miltersen, P.B.: Lower bounds on the size of selection and rank indexes. In: SODA 2005, pp. 11–12 (2005)Google Scholar
  10. 10.
    Munro, J.I., Raman, R., Raman, V., Rao, S.S.: Succinct representations of permutations. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 345–356. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  11. 11.
    Munro, J.I., Raman, V.: Succinct representation of balanced parentheses and static trees. SIAM J. on Comp. 31(3), 762–776 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Munro, J.I., Raman, V., Rao, S.S.: Space efficient suffix trees. J. Alg. 39(2), 205–222 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    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)CrossRefGoogle Scholar
  14. 14.
    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)CrossRefGoogle Scholar
  15. 15.
    Sadakane, K.: Succinct representations of lcp information and improvements in the compressed suffix arrays. In: SODA 2002, pp. 225–232 (2002)Google Scholar
  16. 16.
    Turan, G.: Succinct representations of graphs. Disc. App. Math. 8, 289–294 (1984)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Dong Kyue Kim
    • 1
  • Joong Chae Na
    • 2
  • Ji Eun Kim
    • 1
  • Kunsoo Park
    • 2
  1. 1.School of Electrical and Computer EngineeringPusan National University 
  2. 2.School of Computer Science and EngineeringSeoul National University 

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