Encodings for Range Selection and Top-k Queries

  • Roberto Grossi
  • John Iacono
  • Gonzalo Navarro
  • Rajeev Raman
  • Satti Srinivasa Rao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8125)


We study the problem of encoding the positions the top-k elements of an array A[1..n] for a given parameter 1 ≤ k ≤ n. Specifically, for any i and j, we wish create a data structure that reports the positions of the largest k elements in A[i..j] in decreasing order, without accessing A at query time. This is a natural extension of the well-known encoding range-maxima query problem, where only the position of the maximum in A[i..j] is sought, and finds applications in document retrieval and ranking. We give (sometimes tight) upper and lower bounds for this problem and some variants thereof.


Query Time Split Point Range Selection Inverted List Distinct Symbol 
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.
    Belazzougui, D., Boldi, P., Pagh, R., Vigna, S.: Monotone minimal perfect hashing: searching a sorted table with o(1) accesses. In: Proc. SODA, pp. 785–794 (2009)Google Scholar
  2. 2.
    Bender, M., Farach-Colton, M.: The level ancestor problem simplified. Theor. Comp. Sci. 321(1), 5–12 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Berkman, O., Vishkin, U.: Recursive star-tree parallel data structure. SIAM J. Comp. 22(2), 221–242 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Brodal, G.S., Fagerberg, R., Greve, M., López-Ortiz, A.: Online sorted range reporting. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 173–182. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. 5.
    Brodal, G., Gfeller, B., Jørgensen, A., Sanders, P.: Towards optimal range medians. Theor. Comp. Sci. 412(24), 2588–2601 (2011)zbMATHCrossRefGoogle Scholar
  6. 6.
    Chan, T., Wilkinson, B.: Adaptive and approximate orthogonal range counting. In: Proc. SODA, pp. 241–251 (2013)Google Scholar
  7. 7.
    Clark, D.: Compact Pat Trees. Ph.D. thesis, Univ. of Waterloo, Canada (1996)Google Scholar
  8. 8.
    Fischer, J., Heun, V.: Space-efficient preprocessing schemes for range minimum queries on static arrays. SIAM J. Comp. 40(2), 465–492 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Gagie, T., Navarro, G., Puglisi, S.: New algorithms on wavelet trees and applications to information retrieval. Theor. Comp. Sci., 426–427, 25–41 (2012)Google Scholar
  10. 10.
    Gagie, T., Puglisi, S., Turpin, A.: Range quantile queries: another virtue of wavelet trees. In: Karlgren, J., Tarhio, J., Hyyrö, H. (eds.) SPIRE 2009. LNCS, vol. 5721, pp. 1–6. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  11. 11.
    Golynski, A., Munro, I., Rao, S.: Rank/select operations on large alphabets: a tool for text indexing. In: Proc. SODA, pp. 368–373 (2006)Google Scholar
  12. 12.
    Harel, D., Tarjan, R.: Fast algorithms for finding nearest common ancestors. SIAM J. Comp. 13(2), 338–355 (1984)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Hsu, P., Ottaviano, G.: Space-efficient data structures for top-k completion. In: Proc. WWW, pp. 583–594 (2013)Google Scholar
  14. 14.
    Jørgensen, A., Larsen, K.: Range selection and median: Tight cell probe lower bounds and adaptive data structures. In: Proc. SODA, pp. 805–813 (2011)Google Scholar
  15. 15.
    Li, G., Ji, S., Li, C., Feng, J.: Efficient type-ahead search on relational data: a tastier approach. In: Proc. SIGMOD, pp. 695–706. ACM (2009)Google Scholar
  16. 16.
    Munro, I.: Tables. In: Chandru, V., Vinay, V. (eds.) FSTTCS 1996. LNCS, vol. 1180, pp. 37–42. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  17. 17.
    Pǎtraşcu, M.: Succincter. In: Proc. FOCS, pp. 305–313 (2008)Google Scholar
  18. 18.
    Raman, R., Raman, V., Rao, S.S.: Succinct indexable dictionaries with applications to encoding k-ary trees, prefix sums and multisets. ACM Trans. Alg. 2(4), 43:1–43:25 (2007)Google Scholar
  19. 19.
    Sadakane, K.: Succinct representations of lcp information and improvements in the compressed suffix arrays. In: Proc. SODA, pp. 225–232 (2002)Google Scholar
  20. 20.
    Sadakane, K., Navarro, G.: Fully-functional succinct trees. In: Proc. SODA, pp. 134–149 (2010)Google Scholar
  21. 21.
    Vuillemin, J.: A unifying look at data structures. Comm. ACM 23(4), 229–239 (1980)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Roberto Grossi
    • 1
  • John Iacono
    • 2
  • Gonzalo Navarro
    • 3
  • Rajeev Raman
    • 4
  • Satti Srinivasa Rao
    • 5
  1. 1.Dip. di InformaticaUniv. of PisaItaly
  2. 2.Dept. of Comp. Sci. and Eng.Polytechnic Institute of New York Univ.USA
  3. 3.Dept. of Comp. Sci.Univ. of ChileChile
  4. 4.Dept. of Comp. Sci.Univ. of LeicesterUK
  5. 5.School of Comp. Sci. and Eng.Seoul National Univ.South Korea

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